Methods, devices and systems for determining a target path

ABSTRACT

Aspects of the subject disclosure may include, for example, embodiments and a method. The method includes iteratively providing messages to each Node Processor. Each Node Processor represents a node of a group of nodes. The iteratively providing of the messages comprises providing first messages. Each first message includes a cost associated with a path of nodes visited by each first message. A selected path is obtained from each node having a lowest cost of a group of common endpoint costs for paths having common endpoints. A next group of messages includes the selected path. The iteratively providing of the messages results in selected paths. Also, the method include determining a target path from a remaining path. Other embodiments are disclosed.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/228,017 filed on Apr. 12, 2021, which is a continuation-in-part ofU.S. patent application Ser. No. 16/998,813 (now U.S. Pat. No.11,218,403) filed on Aug. 20, 2020, which is a continuation of U.S.patent application Ser. No. 16/159,239 (now U.S. Pat. No. 10,812,371)filed on Oct. 12, 2018. All sections of the aforementionedapplication(s) and/or patent(s) are incorporated herein by reference intheir entirety.

FIELD OF THE DISCLOSURE

The subject disclosure relates to methods, devices, and systems fordetermining a target path for a network.

BACKGROUND

The traveling salesman problem is one in which a target path is foundbetween a starting point and stopping point with several intermediatenodes. The target path can be a shortest path or most efficient path.Further, the target path includes each and every one of the intermediatenodes. In addition, the starting point and stopping point can be thesame node. The calculating of the target path can require manycomputations and take significant time and processing resources.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made to the accompanying drawings, which are notnecessarily drawn to scale, and wherein:

FIG. 1 is a block diagram illustrating an example, non-limitingembodiment of a communications network in accordance with variousaspects described herein.

FIGS. 2A-2F are block diagrams and associated paths illustrating anexample, non-limiting embodiment of a system functioning within thecommunication network of FIG. 1 in accordance with various aspectsdescribed herein.

FIGS. 2G-2O, 2Y and 2Z are diagrams of associated paths illustrating anexample, non-limiting embodiment of systems functioning within thecommunication network of FIG. 1 in accordance with various aspectsdescribed herein.

FIG. 2P depicts an illustrative embodiment of a method in accordancewith various aspects described herein.

FIGS. 2Q-2U are block diagrams and associated paths illustrating anexample, non-limiting embodiment of a system functioning within thecommunication network of FIG. 1 in accordance with various aspectsdescribed herein.

FIGS. 2V-2X depict illustrative embodiments of methods in accordancewith various aspects described herein.

FIG. 3 is a block diagram illustrating an example, non-limitingembodiment of a virtualized communication network in accordance withvarious aspects described herein.

FIG. 4 is a block diagram of an example, non-limiting embodiment of acomputing environment in accordance with various aspects describedherein.

FIG. 5 is a block diagram of an example, non-limiting embodiment of amobile network platform in accordance with various aspects describedherein.

FIG. 6 is a block diagram of an example, non-limiting embodiment of acommunication device in accordance with various aspects describedherein.

DETAILED DESCRIPTION

The subject disclosure describes, among other things, illustrativeembodiments iteratively providing, from a Message Handler of aprocessing system, messages to each of a group of Node Processors of theprocessing system. Each of the group of Node Processors represents anode of a group of nodes also called a graph of the nodes. Theiteratively providing of the messages comprises providing, by theMessage Handler to a Node Bus, a group of first messages. Each firstmessage includes a cost associated with a path of nodes visited by eachfirst message. Further, the iteratively providing of the messagescomprises determining, by each of the group of Node Processors, pathshaving common endpoints among a portion of the group of first messages,identifying, by each of the group of Node Processors, a cost for each ofthe paths having common endpoints resulting in a group of commonendpoint costs, identifying, by each of the group of Node Processors, alowest cost from among the group of common endpoint costs, identifying,by each of the group of Node Processors, a selected path associated withthe lowest cost, wherein a next group of messages includes the selectedpath. The iteratively providing of the messages results in rejected orpruned paths having higher costs among any set of paths traversing acommon set of nodes. Also, embodiments include determining, by theprocessing system, a target path remaining after pruning pathsthroughout the graph of nodes. Other embodiments are described in thesubject disclosure.

One or more of the techniques described herein can be applied to varioustypes of optimization problems that seek to more efficiently utilizeresources where costs associated with those resources are known. One ormore solutions to the particular problem can be determined according tothe exemplary embodiments described herein.

One or more aspects of the subject disclosure include a method. Themethod, comprising iteratively providing, from a Message Handler of aprocessing system, messages to each of a group of Node Processors of theprocessing system. Each of the group of Node Processors represents anode of a group of nodes. The iteratively providing of the messagescomprises providing, by the Message Handler to a Node Bus, a group offirst messages. Each first message includes a cost associated with apath of nodes visited by each first message. Further, the iterativelyproviding of the messages comprises determining, by each of the group ofNode Processors, paths having common endpoints among a portion of thegroup of first messages, identifying, by each of the group of NodeProcessors, a cost for each of the paths having common endpointsresulting in a group of common endpoint costs, identifying, by each ofthe group of Node Processors, a lowest cost from among the group ofcommon endpoint costs, identifying, by each of the group of NodeProcessors, a selected path associated with the lowest cost, wherein anext group of messages includes the selected path. The iterativelyproviding of the messages results in rejected or pruned paths havinghigher costs among any set of paths traversing a common set of nodes.Further, the method comprises determining, by the processing system, atarget path remaining after pruning paths throughout the graph of nodes.

One or more aspects of the subject disclosure include a device, aprocessing system including a processor, a group of Node Processors, anda Message Handler. Each of the group of Node Processors represents anode of a group of nodes. A memory that stores executable instructionsthat, when executed by the processing system, facilitates performance ofoperations. The operations comprising iteratively providing messages toeach of the group of Node Processors. The iteratively providing of themessages comprises providing a group of first messages by the MessageHandler to a Node Bus. Each first message includes a cost associatedwith a path of nodes visited by each first message. Further, theiteratively providing of the messages comprises determining by each ofthe group of Node Processors, paths having common endpoints among aportion of the group of first messages, identifying by each of the groupof Node Processors, a cost for each of the paths having common endpointsresulting in a group of common endpoints costs, identifying by each ofthe group of Node Processors a lowest cost from among the group ofcommon endpoint costs, identifying by each of the group of NodeProcessors a selected path associated with the lowest cost. A next groupof messages includes the selected path. The iteratively providing of themessages results in a rejected or pruned paths having higher costs amongany set of paths traversing a common set of nodes. Operations caninclude determining a target path remaining after pruning pathsthroughout the graph of nodes.

One or more aspects of the subject disclosure include a machine-readablemedium, comprising executable instructions that, when executed by aprocessing system including a processor, a group of Node Processors, anda Message Handler. Each of the group of Node Processors represents anode of a group of nodes, facilitate performance of operations. Theoperations comprise iteratively providing messages to each of the groupof Node Processors. The iteratively providing of the messages comprisesproviding a group of first messages by the Message Handler to a NodeBus. Each first message includes a quantifiable metric associated with apath of nodes visited by each first message. Further, the iterativelyproviding of the messages comprises determining by each of the group ofNode Processors, paths having common endpoints among a portion of thegroup of first messages. Each of the paths having common endpointstraverses a same subgroup of the group of nodes. In addition, theiteratively providing of the messages comprises identifying by each ofthe group of Node Processors, a quantifiable metric for each of thepaths having common endpoints resulting in a group of common endpointquantifiable metrics, identifying by each of the group of NodeProcessors a lowest quantifiable metric from among the group of commonendpoint quantifiable metrics, identifying by each of the group of NodeProcessors a selected path associated with the lowest quantifiablemetric. A next group of messages includes the selected path. Theiteratively providing of the messages results in a rejected or prunedpaths having higher costs among any set of paths traversing a common setof nodes. Operations can include determining a target path remainingafter pruning paths throughout the graph of nodes. Referring now to FIG.1 , a block diagram is shown illustrating an example, non-limitingembodiment of a communications network 100 in accordance with variousaspects described herein. System 200 in FIG. 2A and the systems in FIGS.2H-2M can be located in communication network 100 and implement themethod 260 as described herein.

In particular, a communications network 125 is presented for providingbroadband access 110 to a plurality of data terminals 114 via accessterminal 112, wireless access 120 to a plurality of mobile devices 124and vehicle 126 via base station or access point 122, voice access 130to a plurality of telephony devices 134, via switching device 132 and/ormedia access 140 to a plurality of audio/video display devices 144 viamedia terminal 142. In addition, communication network 125 is coupled toone or more content sources 175 of audio, video, graphics, text and/orother media. While broadband access 110, wireless access 120, voiceaccess 130 and media access 140 are shown separately, one or more ofthese forms of access can be combined to provide multiple accessservices to a single client device (e.g., mobile devices 124 can receivemedia content via media terminal 142, data terminal 114 can be providedvoice access via switching device 132, and so on).

The communications network 125 includes a plurality of network elements(NE) 150, 152, 154, 156, etc. for facilitating the broadband access 110,wireless access 120, voice access 130, media access 140 and/or thedistribution of content from content sources 175. The communicationsnetwork 125 can include a circuit switched or packet switched network, avoice over Internet protocol (VoIP) network, Internet protocol (IP)network, a cable network, a passive or active optical network, a 4G, 5G,or higher generation wireless access network, WIMAX network,UltraWideband network, personal area network or other wireless accessnetwork, a broadcast satellite network and/or other communicationsnetwork.

In various embodiments, the access terminal 112 can include a digitalsubscriber line access multiplexer (DSLAM), cable modem terminationsystem (CMTS), optical line terminal (OLT) and/or other access terminal.The data terminals 114 can include personal computers, laptop computers,netbook computers, tablets or other computing devices along with digitalsubscriber line (DSL) modems, data over coax service interfacespecification (DOCSIS) modems or other cable modems, a wireless modemsuch as a 4G, 5G, or higher generation modem, an optical modem and/orother access devices.

In various embodiments, the base station or access point 122 can includea 4G, 5G, or higher generation base station, an access point thatoperates via an 802.11 standard such as 802.11n, 802.11ac or otherwireless access terminal. The mobile devices 124 can include mobilephones, e-readers, tablets, phablets, wireless modems, and/or othermobile computing devices.

In various embodiments, the switching device 132 can include a privatebranch exchange or central office switch, a media services gateway, VoIPgateway or other gateway device and/or other switching device. Thetelephony devices 134 can include traditional telephones (with orwithout a terminal adapter), VoIP telephones and/or other telephonydevices.

In various embodiments, the media terminal 142 can include a cablehead-end or other TV head-end, a satellite receiver, gateway or othermedia terminal 142. The display devices 144 can include televisions withor without a set top box, personal computers and/or other displaydevices.

In various embodiments, the content sources 175 include broadcasttelevision and radio sources, video on demand platforms and streamingvideo and audio services platforms, one or more content data networks,data servers, web servers and other content servers, and/or othersources of media.

In various embodiments, the communications network 125 can includewired, optical and/or wireless links and the network elements 150, 152,154, 156, etc. can include service switching points, signal transferpoints, service control points, network gateways, media distributionhubs, servers, firewalls, routers, edge devices, switches and othernetwork nodes for routing and controlling communications traffic overwired, optical and wireless links as part of the Internet and otherpublic networks as well as one or more private networks, for managingsubscriber access, for billing and network management and for supportingother network functions.

FIGS. 2A-2F are block diagrams and associated paths illustrating anexample, non-limiting embodiment of a system functioning within thecommunication network of FIG. 1 in accordance with various aspectsdescribed herein. Further, the embodiments shown in FIGS. 2A-2Fillustrate a concept of pruning paths in calculating a target path (thatcan be a complete shortest path). Pruning can include discardingintermediate paths that may be costlier than less costly intermediatepaths. Referring to FIG. 2A, the system 200 comprises group nodes202-218 including a source node 202, an intermediate 210, and adestination node 218, all of which interconnected to each other. Infurther embodiments, the group of nodes 202-218 may be processors (i.e.Node Processors) in a computing/processing environment including a cloudcomputing environment and/or virtual computing environment. Inadditional embodiments, the group of nodes may be network elements in acommunication network. In some embodiments, the second destination nodecan be the same node as the source node. Further, an intermediate node210 can be identified as node within the group of nodes 202-218 that istraversed between a first portion of the group of nodes 209 and a secondportion of the group of nodes 219. The group of nodes can be a networkof nodes or a collection of nodes each of which implement functions(some of which may be the same). The embodiments shown in FIG. 2A-2F useintermediate node 210 as an example node to illustrate pruningintermediate paths in calculating a target path (e.g. complete shortestpath).

In one or more embodiments, a server (or group of servers) that can beone or a portion of the group of nodes 202-218 can determine a targetpath between the source node 202 and the destination node 218 thatincludes each of the nodes (204-216). In addition, the server can be anadministration service or processor separate or outside of the group ofnodes though the preferred embodiment is for each node in the graph ofnodes to be represented by its own server or computer processor called aNode Processor. Further, the servers can identify a first target pathfor the first portion of the group of nodes 209 and identify a secondtarget path for a second portion of the first group of nodes 219. Thefirst target path or second target path can be a shortest path or a mostefficient path. The first target path and the second target path can becombined to determine an overall target path. However, note that everyintermediate node conducts pruning at the same time such that althoughFIGS. 2A-2F show the pruning from the perspective of intermediate node210, each node 204-216 conducts pruning and an overall target path canbe determined as the remaining shortest path after all pruningoperations are completed.

In one or more embodiments, each link between two nodes in the group ofnodes can be associated with a cost. For example, the cost between thesource node 202 and node A 204 can be 4. The cost, which can also be anyquantifiable metric, can be a term that can be include the time for dataor message to travel, distance, monetary cost, available bandwidth,latency, throughput, risk, probability-of-success or any other metricfrom one node to another.

In one or more embodiments, each node can be a Node Processor within acomputing environment. Any Node Processor can receive a messageoriginating from another Node Processor and having an accumulated costfrom the totality of node travels up to the other node which originatesthe message. The current Node Processor adds to the prior accumulatedcost, the cost of travel between the node originating the message andthe current node. Further, the Node Processor may request a MessageHandler to drop a message onto a communication bus of the computingenvironment, receivable by other Node Processors in the computingenvironment. In this embodiment, Node Processors do not directlycommunicate with one another, but instead via a Message Handler thatcoordinates message flows on a common communication bus. For example,node A 204 can receive several messages. A first message can be receiveddirectly from the source node 202 at a cost of 2. In response toreceiving the first message, node A 204 can forward provide a message toa communication bus which is received by node B 206 with accumulatedcosts of 3 and the intermediate node 210 with accumulated costs of 5. Asecond message received by node A 204 can be from the source node 202and node B 206 at a cost of 5. In response to receiving the secondmessage, node A 204 can provide a message which can be received bysource node 202 and the intermediate node 210. The message travelingbetween nodes carries a history of node visitations and the source node202, being part of the travel history, ignore the message from node A204 which traveled from source node 202 via node B 206 and then to nodeA 204. Alternatively, intermediate node 210 receives the same messageand does not ignore it, because the same node has not been visitedpreviously as evidenced in the visitation record in the message. A thirdmessage is received by node A 204 from source node 202, node C 208, andnode B at a cost of 6. In response to receiving the third message, nodeA 204 can forward a message to source node 202 and the intermediate node210. Again, source node 202 ignores this message due to its own presencein the travel history evidenced in the visitation record in the message.Intermediate node 210 can know from the visitation records in each ofthe received messages that one message traversed only the source node202 and one other node A 204. One other message added node B 206 and thethird message also added node C 208. Therefore, the three messagesreceived by the intermediate node 210 do not present the same set ofvisited nodes.

Referring to FIG. 2B, in one or more embodiments, the cost of each ofthe different, multiple paths within the group of nodes are calculatedand listed for the first portion of the group of nodes 209. The NodeProcessor for node 210 compares the cost for all messages including acomplete path from source node 202 to node 210 and having visited allother intermediate nodes in-between being node A 204, node B 206, andnode C 208. Comparisons of path costs, conducted by any Node Processor,must be for paths having the same visited set of nodes. Aftercalculating different, multiple paths, the path source node-node C-nodeB-node A-intermediate node is the first target path for the firstportion of the group of nodes 209.

Referring to FIG. 2C, the target path 203, source node-node C-nodeB-node A-intermediate node is highlighted for the first portion of thegroup of nodes 209. Thus, the overall target path between the sourcenode 202 and the destination node 218 can include the first target path203 of the first portion of the group of nodes 209. Further, indetermining the overall target path that includes all nodes 202-218, aserver can forgo calculating the cost of any first target path thatincludes a path in the first portion of the group of nodes other thanpath 203. For example, any path between the source node 202 and thedestination node 218 that includes the path source node-node A-nodeB-node C-intermedia node cannot be a target path between the source node202 and the destination node and is not used to compute the overalltarget path between the source node 202 and the destination node 218.Intermediate node 210, having received multiple messages from the firstportion of the group of nodes 209 including longer paths than path 203does not provide any corresponding messages onto the communication busfor such longer paths, thereby effectively terminating any subsequentcomputation that would otherwise include them. The elimination ofmessaging to the communication bus, effects the concept of pruning ofpaths. Thus, from a point of view, the server or Node Processor forintermediate node 210 is able to prune or eliminate the number ofcalculations to determine the overall target path between the sourcenode 202 and the destination node 218 by determining the first targetpath 203 of the first portion of the group of nodes 209. The target pathcan be a shortest path or a most efficient path.

Referring to FIG. 2D, in one or more embodiments, the cost of each ofthe different, multiple paths within the group of nodes are calculatedand listed for the second portion of the group of nodes 219. Aftercalculating different, multiple paths, the path intermediate node-nodeD-node E-node F-destination node is the second target path for thesecond portion of the group of nodes 219. The computation of the secondtarget path occurs after the computation of the first target path 203and should be considered as an extension of the first target path.

Referring to FIG. 2E, the target path 213, intermediate node-node D-nodeE-node F-destination is highlighted for the second portion of the groupof nodes 219. Thus, the overall target path between the source node 202and the destination node 218 can include the first target path 203 ofthe first portion of the group of nodes 209 and the second target path213 of the second portion of the group of nodes 219. The overall targetpath is the combination of first target path 203 and second target path213, which can be a complete path and/or shortest/most efficient paththrough the graph of all nodes 200.

Referring to FIG. 2F, the cost, in terms of time, is listed for eachpath in the group of nodes. Each path is listed according to an indexfor reference. Further, the calculation of paths are sequenced accordingto cost in terms of time. Note, in some embodiments, the cost of timedoes not indicate the amount of time to determine the cost of path. Insuch embodiments the cost of time is an indicator of when to placemessages on the Node Bus to be received by all Node Processors which maythen process costs by accumulating total travel costs and comparing thecosts for messages associated with multiple paths having the same groupsof visited nodes.

As listed in index 12, the first target path 203 for the first portionof the group of nodes is calculated with cost 9, with the first targetpath 203 being source node-node C-node B-node A-intermediate node.Further, the intermediate node 210 continues to provide to a messagingbus, messages that can be received by nodes D 212, node E 214, and nodeF 216 until index 16, with includes the path source node-node A-nodeB-node C-intermediate node. The path for index 16 traverses the samenodes as the first target path 203, but has more cost. Thus, theintermediate node 210 may not forward any messages from any other pathtraversing the set of nodes source node, node A, node B, node C, andintermediate node other than the path of index 12. Thus, the NodeProcessor for the intermediate node provides a message for the messagingbus corresponding to index 12, but not one for index 16. Terminating themessage flow for index 16 and any other path containing the nodes sourcenode, node A, node B, node C, intermediate node and having higher costthan index 12 removes subsequent calculations for every possible targetpath that would have otherwise used the paths for those indexes. AnyNode Processor can prune (stop messaging) for all but one path having acommon set of visited nodes. The intermediate Node Processor, can prunethe paths for indices 16, 20, 21, 27, and 31, after observing the costfor each of these paths is higher than that of index 12, by terminatingmessage flows from the intermediate node process to the messaging busfor these paths, thereby eliminating all subsequent calculations thatwould otherwise include these paths.

As listed in index 34, the overall target path (i.e. combination offirst path 203 and second target path 213) is calculated by theDestination node processor 218 with cost 18, and includes the pathsource-node C-node B-node A-intermediate node-node D-node E-nodeF-destination node. The cost 18 is the first observed cost for thiscomplete path and is stored by Destination node processor for comparisonto costs for other equivalent paths containing the same set of visitednodes. If any other path with the same set of nodes has a higher cost,then Destination node processor prunes those paths by terminatingmessaging including such paths to the messaging bus. For example, thepath for index 40 traverses the same nodes as the path from index 34,but has more cost 22. The Destination node processor 218 does notforward the message from index 40 to the Message Handler, therebyeffectively pruning the path for index 40. If the Destination nodeprocessor 218 is the last node in the graph of all nodes, then it issynonymous with being the Stop Node and a Stop Node, observing alowest-cost, complete path through the entire graph of nodes announcesto all Node Processors that a solution has been found, which then causesall Node Processors to cease processing. This eliminates all subsequentcomputational costs that would otherwise occur. Also being of highercosts than the path of index 34, the paths associated with indices 41,42, and 43, are pruned (terminated) by the Destination node processor.

In one or more embodiments, the cost for each of the first plurality ofpaths comprises an available bandwidth between the source node, each ofthe first group of intermediate nodes, and the first destination node,wherein the cost for each of the second plurality of paths comprises anavailable bandwidth between the first destination node, each of thesecond group of intermediate nodes, and the second destination node. Infurther embodiments, the source node, the first destination node, thesecond destination node, the first group of intermediate nodes, and thesecond group of intermediate nodes comprise a network element in acommunication network.

Further, portions of embodiments can be combined with portions of otherembodiments.

In one or more embodiments, to calculate the shortest path through eachnode in a computing environment, a signal (electrical or optical) islaunched into the computing environment (circuit) having componentsrepresenting the nodes to be visited. The signal would move as fast asthe path would allow it to. With each node visit, the signal would bemodified to reflect the visitation. Such a signal moves between thenodes, flowing like waves on a transmission line or a swimming pool. Tomake the computing environment behave this way, the architecture of thecomputing environment allocates a computing resource to each node thatwould receive messages from other nodes and rebroadcast them in a mannerto reflect the visitation. In this manner, signals launch as waves thatwould automatically move between the nodes without supervision from asingle computer resource. No single node has complete knowledge ofactions of the other nodes, but handles its own piece of the overallcomputation, independent of other processors (nodes). Such a method orsystem can be designated as crowd processing and it is distinct fromdistributed computing, which shares a computing task among manycomputing devices, but still under the supervision of a master computingdevice. The nodes communicate with each other, building path knowledgealong the way. A Stop Node (a final destination node—can be the same asthe Start Node (e.g. source node)) processor listens for a message fromany Node Processor that must have two properties to find and assert thetarget path through the graph of all nodes. The first property is thatthe message would announce that it had visited all possible nodes(complete path), and the second property is that the message would havethe lowest travel time among all complete paths. Such embodiments can betime-based, indicating that the message pertaining to the shortest totalpath, the target path, is presented on the messaging bus before manyother messages have traveled a complete path. Once this first completepath of the message is found by the Stop Processor, all remainingcomputation can cease because the solution has been found. Again, thisis a distinctly different concept than a computer analyzing allpossibilities and finding the best one. There is no centralizedcomputing resource controlling the calculation of the shortest completepath. A message (wave) is launched and every member of the graph ofnodes communicate among themselves and when the lowest cost (time) pathis presented, the calculation of the shortest complete path is done. Insuch embodiments, the solution presents itself as a natural consequenceof the flow of messages traveling through all the available nodescomprising the graph of nodes.

Conventional techniques for solving the shortest path through each nodeof a group of nodes cause each possible path among the nodes to beassigned a computing thread or central processing unit (CPU). Even withmoderately sized groups of nodes, the total number of threads or CPUsthat must be managed can exceed the administrative capability ofoperating systems of the computing environments for the group of nodes.Embodiments described herein instead assigns exactly one computingresource to each node, one for the Stop Node (which may be coincidentwith the Start Node), a Message Handler, and an Administration Processorthat provides initial conditions to all other processors and aninitialization message to start the processing task. With a one thousandnode group, one thousand processing threads are assigned potentiallyacross many servers that do not need to be under the control of a singlecomputer. Conventional techniques may need billions or trillions ofcomputing threads, which require swapping and time-sharing of the memoryand CPU resources.

For embodiments described herein, the terms distance, time, and cost canbe interchanged as the accumulating measure while the messages traversethe Node Processors. Embodiments can keep track of an accumulatingquantity that could be a representation of distance, time, cost, oranything else that could be numerically accumulated. Embodiments canhandle both perfect and approximate solutions. A perfect solution is onewhere travel can occur between any pair of nodes in the graph of allnodes. An approximate solution is one where travel between nodes isconstrained (such as being limited to nearby nodes). Determining thatcertain paths cannot yield the shortest path, allows pruning of thosepaths and all larger paths including those paths up to complete paths.Path pruning early in the flow of messaging has a more significanteffect on the elimination of subsequent processing than pruning later inthe messaging flow. Referencing FIG. 2G, this is akin to pruning a largetrunk of a tree as opposed to pruning a twig at the top of the tree.Every twig represents a computable path and pruning a large branch caneliminate millions of twigs or paths. Given the factorial (n!) growth incomputational cost of the traveling salesman problem and relatedproblems with n nodes, graphs with even hundreds of nodes can presentintractably large computational costs. Some embodiments provide forlarge scale pruning of message flows by every node in the graph suchthat the composite reduction in total computational costs approacheslinear growth with the number of nodes, rather than factorial growth.Benefits of some embodiments can include the ability to stop computationonce a complete, shortest path is found, thereby eliminating remainingcomputations. For example, consider any set of visited nodes, includingn nodes plus the START and STOP nodes. Exactly n!−1 branches can bepruned between START and STOP. This ability is based on a basic propertyof the geometry and embodiments herein exploiting it. Given any fourlocations (including two nodes, START, and STOP) one complete path canbe pruned between START and STOP. For example, given nodes A, B, C, andD, a message can travel from A to D two ways, ABCD or ACBD. These twopaths either have exactly the same length or one is longer. If, forexample, ACBD is longer than ABCD, it can be seen that any pathincluding the sequence ACBD could be shorter if that path used ABCDinstead (and all other prior or subsequent nodes visits were exactly thesame). This shows that any path sequence containing ACBD cannot be thetarget path, so any computation for any path containing ACBD can beterminated. If both paths ABCD and ACBD are equal length, one can bepicked (e.g. based on a logical value such as a processor ID) and theother ignored. The task is to find “a” lowest cost path, not all equallylowest cost paths. Similarly, among any four nodes one of two possiblepaths can be pruned from A to B (traversing C and D), A to C (traversingB and D), B to C (traversing A and D), B to D (traversing A and C), andC to D (traversing A and B). There is another attribute of someembodiments which applies when the cost of traveling between any twonodes is bilateral. This means that distance or cost ABC is exactly thesame as CBA. If path ABCD has a lower cost than ACBD, then we can usethis argument to claim that path DCBA has a lower cost than DBCA. Thismeans any path can be pruned containing the sequences ACBD or DBCA. Thisallows more opportunities for pruning during processing. FIG. 2G depictsthe pruning of branches and the benefit of finding an early completeshortest path which terminates the remaining processing. Note, in someembodiments, a test run can be done, a priori, to determine an existenceof a complete path where all nodes are visited.

In some embodiments Node Processors can be implemented as processingthreads of one or more computers. Functionality of Node Processors orany other processing of the embodiment can be defined logically orvirtually, e.g. virtual machine.

Referring to FIG. 2H, the system includes several processing componentsincluding an Administration Processor shown in FIG. 2I. TheAdministration Processor asserts to cost of travel between nodes. If theproblem involves computing travel time between geographic nodes, theAdministration Processor knows the geographic locations of start, stop,and all other nodes. The Administration Processor asserts the bilateralcosts/distance/time between them as part of a problem-set-up phase ofprocessing. In the case of the equal bilateral cost assumption betweenall node pairs, a special message is provided by the AdministrationProcessor to other processors to indicate as such. In problems wherevisitations between nodes are constrained leading to an approximateresult rather than an exact result, the Administration Processornotifies each node processor about the local, neighboring nodes that itshould listen to. If the complete, shortest path is approximate, thereis a potential for creating stranded islands of nodes in the graph ofnodes, because the nearest neighbors to all members of a cluster arepart of the cluster and not other clusters. It is possible for nomembers of a cluster to connect to any node outside of the cluster.Therefore, a graph theory mechanism is indicated to find clusters andalso find the lowest cost connections between clusters to ensure a pathto completion and no stranded clusters. The Administration Processoralso initiates the final process to find the lowest cost path. Referringto FIG. 2I, the basic functionality of the Administration Processor isshown whereby it can send cost information to all other processors andalso invoke a first mode of operation to test for the presence of anycomplete path through the node graph as well as a second mode ofoperation which is to find the target path.

Embodiments provide one Node Processor per node. Each Node Processorreceives (from the Administration Processor) a list of other nodes thatare permitted to be in its path (its local neighborhood). For smallgroups of nodes, all Node Processors can listen to each other withmanageable computational impact. For large groups of nodes, restrictingnode connections to a local community is one manner in which to reducecomplexity with relatively low impact on finding a target path, but theresult cannot be guaranteed, only approximated. However, embodimentsdescribed herein work with or without node neighbor constraints. EachNode Processor continuously monitors the Node Bus/buses and receives allof the messages deposited thereon of the form (cost_(total_path),node_mask, pointer, node ID₅, cost₅₄, node ID₄, cost₄₃, node ID₃,cost₃₂, node ID₂, cost₂₁, node ID₁). The node_mask provides an exactvisitation record of all nodes visited and contributing to the cost,cost_(total_path). The node_mask does not show the order of historicalnode visitations. Only the node visitation order for the last five nodesvisited is presented in the message. The remaining elements of themessage provide the sequence and costs of recent node visits to becompared with the contents of other messages by any Node Processor. Atthe start of messaging on the Node Bus, all five historical nodesvisited are exactly the Start Node and costs between them are allexactly zero. When messages have visited three nodes beyond the StartNode comparisons allow pruning to begin. At this depth of processing,Node ID₁, Node ID₂, and Node ID₃ still all indicate the Start Node. OnlyNode ID₅ and Node ID₄ show other node ID₅. A Node Processor inspects thelast five nodes of travel to compare costs for paths with common sets ofnodes between Node ID₁ and the current node. There can 24 distinct pathsto the current node when looking back at the last five nodes visited((depth−1)!). All but one of these paths can be pruned. An embodimentcan be built using longer sequences of prior-visited nodes than five, inwhich case the form of the message would merely be extended using thesame logic. Looking back at the last five visited nodes yieldssignificant pruning opportunities, but with factorial growth in theprocessing by the Node Processors. For instance, looking back six nodeswould allow comparison of 120 paths with all pruned except one, but thecost of comparisons is increasingly as a factorial of depth. Beyondfive, there is a questionable tradeoff between reduction of total pathcomputations and Node Processor processing. The choice of this messagingdepth (number of historical visited nodes) may be a determinablefunction of the size of the node graph and bilaterality of node paircosts. Recall, for exact solution computations, all nodes are neighborsof all other nodes. For each of the Node Bus messages received by anyNode Processor, each Node Processor first checks the last visited nodeID against its neighbor list to determine if it is a permitted neighbor.If not, the message is ignored, otherwise the “node mask” in the messageis inspected for a self-match which could prove this node has alreadybeen visited in the history of the received message. The node mask isbinary and has a position for each node in the graph of nodes. It merelyindicates what nodes have been visited, but does not provide the orderof visitation. If there is no self-match in the node mask, checks arerun by a Node Processor on the sequence of the last 5 node IDs tocompare its node visitation cost with the costs of other node sequencesfrom other messages already received. It does this by comparing the cost(from prior messages) of visiting the same set of the 5 most-recentnodes visited, having the same starting node, but in a differentsequence. For example, a Node Processor may receive a message where thelast five nodes visited are JGECA. This could be compared in terms ofcost to the path GJECA or JGCEA. To compare costs between any twomessages, the final cost to get to the processing node must be included,not just the total cost, cost_(total_path), provided in the receivedmessages. For example, two messages may arrive at Node Processor Fcontaining costs for visiting prior nodes ABCDE and ACBDE respectively.In order to assert the lower cost of the two, the cost of getting to Fmust be included so that the total costs will be for paths ABCDEF andACBDEF respectively. If a lower or equal cost path is observed by a NodeProcessor for a prior message, the current message is ignored, therebyeffecting pruning of the equal or higher cost path presented in themessage. If no lower cost path was previously observed by a NodeProcessor, the current message is updated with the cost to arrive at thecurrent node as well as the shifting of the recent node visitinformation to the right and insertion of the most current node oftravel. The pointer value in the message (which will be discussedfurther) is retained in the updated message. The node mask is thenupdated and the message is sent to the Message Handler processor. TheNode Processor may compute that a path for the current received messagehas a lower cost than a prior path for which an updated message wasalready sent to the Message Handler. In this event, the Node Processorcan send a “delete prior message” request to the Message Handler via theAdministration Bus which then deletes the prior message before placingit on the Node Bus. This action obviates all subsequent processingotherwise associated with the terminated message and its path. To effectthis ability to drop messages already sent to the Message Handler, acritical component of the apparatus is that messages are dropped ontothe Node Bus by the Message Handler with sequentially increasing cost ortime. This guarantees the prior message has not been placed onto theNode Bus yet and can therefore be deleted prior to placement. Whensending messages to the Message Handler, the first Node Processor(number zero) places its message onto the Administration Bus and thenelectrically toggles a line or sends a unique message pattern. This line(or message) is monitored by all Node Processors and is used as a meansof avoiding collisions among Node Processors on the Node Bus. Each NodeProcessor waits its turn as it counts the number of toggles on the line(or sends the unique message). If a Node Processor has no message tosend to the Message Handler, it toggles the line on its turn anyway.When a new message is placed onto the Node Bus by the Message Handler,all Node Processors use this to reset their own toggle counter, observethe new message, conduct required processing, and then wait their turnto report back to the Message Handler. This looping continues until theStop Processor sends a message to all other processors to stopprocessing. Referring to FIG. 2J, it shows the functionality of a NodeProcessor.

A Message Handler comprises a processor that manages the sequence(ranked by increasing time, cost, or distance) of messages it placesonto the Node Bus. The Message Handler receives messages from NodeProcessors over the Administration Bus, receives updated pointers (thatpoint in memory to a sequence of visited node IDs) from the StopProcessor via the Pointer Bus, and then updates messages in the stackwith these updated pointers, ranked by time, distance, or cost and thenplaces the next message in the sequence on the Node Bus after all NodeProcessors have completed reporting pursuant to the prior message placedonto the Node Bus. The Message Handler maintains a stack of nodemessages to be placed onto the Node Bus. When two messages have the samecost, the node ID of the last node visited can be used as an arbiter forordering. For scalability, the stack may be effected as a set of stackswhere each sub-stack holds messages from a prescribed subset of nodes.For example, messages one subset of nodes go to sub-stack 1 whilemessages from another subset of nodes go to sub-stack 2. Doing so allowsthe Message Handler to multi-thread and expedite message insertion anddeletion in the full stack that could otherwise become significant forlarge groups of nodes. The embodiment of a Message Handler may also usea stack ranking architecture where stack subsets can have their ownsubsets in a cascade or arbitrary depth. Using multiple message stacksalso implies that messages cannot be placed onto the Node Bus until thecosts are compared for the “next” message on each sub-stack. This samelogic applies to cascaded sub-stacks of arbitrary depth. For example, ifthe stack has sub-stacks (layer A) and each sub-stack has sub-stacks(layer B) the all layer B sub-stacks must have their “next” messagetime-compared before choosing one for each layer A sub-stack. Then alllayer A times or costs are compared to arrive at a single message whichis the next message to be placed on the Node Bus. Otherwise, messagescould be placed on the Node Bus out of sequence. As described in theembodiments herein, the messages placed onto the Node Bus do not present100% of visited node IDs along the traveled path. The reason is that forlarge groups of nodes, the bandwidth of the Administration Bus and NodeBus would be consumed by this movement of information. Pointers allow usto replace long sequences of node IDs on a traveled path with a pointerto that sequence stored on the Stop Processor. Each time a path has todiverge (branch), a new pointer is created for it by the Stop Processorand the Message Handler is made aware of that path divergence wheninformed by the Stop Processor via the Pointer Bus. The Message Handlercan delete a message from the message stack if requested to do so by aNode Processor, which can happen if the Node Processor discovers ashorter path sequence (from the pruning process) and wants to eliminatea prior message and insert one for the shorter path. Sending any deleteor add message happens when a Node Processor gets its turn tocommunicate on the Administration Bus. After placing a message onto theNode Bus, the Message Handler monitors the toggle line on theAdministration Bus as each Node Processor takes its turn with updatingthe Message Handler (sometimes sending a message and sometimes not butalways toggling the line at the end of its turn). The Message Handlerknows how many Node Processors there are (it was informed at set up bythe Administration Processor), so by observing the toggle counter, itknows when all Node Processors are done working. When it places a newmessage onto the Node Bus, it resets its own toggle counter, as do theNode Processors. Referring to FIG. 2K, it shows the functionality of theMessage Handler.

The Stop Processor monitors the Node Bus messages and uses the node maskto identify when a path has completed visitation to all nodes. Formaximum speed, a completion check on the node mask can be accomplishedin hardware using open collector transistors, tied together in tandemand pulled up to a high (1) voltage state using a pull up resistor. Allof the node mask bits are inverted, so if they are all in a high state(all nodes visited), the inverse is all 0s. This turns off alltransistors, causing the tandem connections at all transistor collectorsto be pulled high by the pull-up resistor. If any node mask bit is 0, atleast one inverted bit will be in a high state, turning on at least onetransistor and pulling V_(out) to a low state. The Stop Processorobserves a complete node visitation mask when V_(out) transitions to ahigh state. (See FIG. 2L).

In a message with a complete node mask, the Stop Processor sees thetotal travel cost to the last node visited. It then adds the cost oftravel between the last node and the Stop Node to the accumulated cost,thereby asserting a “complete cost”. This allows the Stop Processor tohave a potential target path which can be designated as the “currentcandidate target path”. There may be a lower complete cost path thatshows up later on the Node Bus if the cost of travel from its last nodevisited to the Stop Node is lower than for earlier messages. The targetpath must include the cost of the final step to the Stop Node before itcan be asserted as the target path. For example, the Stop Processor maysee a path (start, A, B, C, E, D) which is complete, and then the StopProcessor adds the total cost of travel between D and the Stop Node.Another message with the path (start, A, B, C, D, E) may show up on theNode Bus a bit later, but if the cost from E to the Stop Node is lessthan the cost from D to the Stop Node, the second message may have thelowest complete cost, distance, or time in which case it can replace thecurrent shortest complete path. If not, the later message is ignored.When the Stop Processor sees any message on the Node Bus having a totaltravel cost greater than the cost of the current shortest complete path,then it is not possible for any subsequent message to have a lower totalcost. This is because messages are always placed onto the Node Bus intime or cost-ordered sequence. There can never be another message with alower travel cost presented. Since the Stop Processor can thenpositively know that the current shortest complete path is the “finalshortest complete path”, the Stop Processor then sends a message on theNode Bus to all processors to stop processing and it delivers the “finalshortest complete path” to the Administration Processor via theAdministration Bus. The Stop Processor also manages the pointers toarrays that contain the travelled sequences of nodes for any path. Itmonitors the Administration Bus and receives messages sent from NodeProcessors to the Message Handler. It determines when a path has to besplit and it creates new pointers to the new paths and informs theMessage Handler via the Pointer Bus. Because the Stop Processor performsthe task of pointer maintenance, once it finds a path that has acomplete node mask and the “final shortest complete path”, it uses thecorresponding pointer from that message to look up the exact nodevisitation sequence that it then sends to the Administration Processor.An additional mechanism for stopping all processing is when then MessageHandler sends a message on the Node Bus that it has “no more messages”.If the Stop Processor sees this message, it asserts the current shortestcomplete path to be the final shortest complete path and delivers thesame set of information to the Administration Processor using the nodevisitation sequence pointed to by the last observed pointer.

In referring to the Administration Bus, this communication bus is usedby the Administration Processor to initially inform all Node Processorsabout their node neighbor lists and the bilateral costs of travel to andfrom each of those neighbors, to reset all processing, clear counters,clear pointers, and inform each Node Processor about its node ID and toinform the Stop Processor and Message Handler about the total nodecount. This bus is also used by the Stop Processor to send the shortestcomplete path (the target path) to the Administration Processor at theconclusion of processing.

The Node Bus is used by the Message Handler to broadcast messages (fromindividual Node Processors) to all Node Processors. The messages placedon the Node Bus are placed in rank order of cost, time, or distance,thereby achieving the “flow” character of the embodiments describeherein. It is this flow character that allows one to unequivocally knowwhen it is impossible for any remaining path to have a lower cost, time,or distance than the “current shortest complete path”.

The Pointer Bus is a communication bus used to communicate pointersbetween the Stop Processor and the Message Handler. The Message Handlermay send queries to the Stop Processor to update a pointer if needed orthe Stop Processor may proactively send an update to the Message Handleron the same bus.

The upper bounds to the embodiments described herein are set by thebandwidth of these communication buses, so multiple instances of each ofthese buses are allowed, thereby permitting scalability.

In an exemplary embodiment, to prepare for processing, theAdministration Processor determines for every node, what its neighbornodes should be up to and including all other nodes. The AdministrationProcessor also determines the bilateral time, distances, or costs oftraveling between all node pairs that are neighbors. These neighborrelationships and costs are sent via the Administration Bus and are heldin memory by the Node Processors.

After all pre-processing tasks are completed, the AdministrationProcessor initiates the path length computations by sending a startmessage to the Message Handler on the Administration Bus. This startmessage has a start time of 0, includes a node mask which is all zeros(with optionally a single one representing the Start Node), a pointer(explained below) of 0, and includes a node ID=0 for each of the lastfive node IDs visited (each being the Start Node) and sends incrementaltravel costs between nodes of 0. The message appears in the generalform: 0,0000000000000000000000000,0,0,0,0,0,0,0,0,0,0 (accumulated totalcost, mask, pointer, node ID5, cost54, node ID4, cost43, node ID3,cost32, node ID2, cost21, node ID1. The Message Handler immediatelyplaces this message on the Node Bus to begin processing. The StopProcessor observes this initial message on the Node Bus and creates afirst pointer, called 0, pointing to an in-memory array on the StopProcessor with the single value “0” (denoting the Start Node). TheMessage Handler sets its own toggle counter to zero and all NodeProcessors, seeing the new message (total cost=0) on the Node Bus, alsoset their own toggle counters to zero.

Each Node Processor is constantly listening for messages on the Node Busand conducts processing for messages originating from its “neighbornodes” (as determined and announced by the Administration Processor viathe Administration Bus during pre-processing). The first step ofprocessing is to inspect the node mask to ensure the message has not yettraversed that node. Each node may only be visited once, so a priorvisit to the node causes the message to be ignored. The Message Handlerplaces messages on the Node Bus sequentially in time, cost, or distanceas non-limiting examples. This does not mean that it places the messageson the Node Bus at the prescribed time, but instead in ascendingsequence. In one or more embodiments, this temporal character can besignificant or critical to the particular embodiment because it is wherethe “flow” characteristic is achieved, mimicking the flow of a signalthrough a circuit or waves moving on a surface.

If a received message passes these tests, the last five node IDs andtravel costs are checked for path pruning opportunities. FIG. 2M shows asimple example of two possible paths between start and node C,traversing node A and node B where only one path is ultimately allowedto be used.

To accomplish this pruning test, the Node Processor checks to see if ithas stored a copy of a message previously sent to the Message Handlerwith the same node IDs as are contained in the currently receivedmessage and having the same node ID₁. This means the start of thefive-node path begins at the same node and ends with the current nodeand the paths have the same visited nodes in between. If the NodeProcessor finds such a comparable prior message, it compares the totalcost of travel to the current node for both messages. If the priormessage has the lower or equal cost, the current message is discardedand nothing is sent to the Message Handler. Otherwise, a message is sentto the Message Handler to delete the prior message and the NodeProcessor sends a new message to the Message Handler after updating thetotal cost/time/distance (up to the current node), updating the nodemask, retaining the same pointer, and FIFO (first in, first out)shifting the node IDs and incremental costs to the right in order toinsert the current node ID and incremental cost from the last node ID.This new message is sent to the Message Handler on the AdministrationBus. It does so on its turn which is determined when the toggle countmatches its own node ID.

The comparison of costs among the most recently visited five nodesallows for pruning of up to 23 paths between node ID1 (from the receivedmessage) and the current node. Various embodiments may use differentprocessing depths. A minimum depth of three nodes is required forpruning travel paths. If the depth of nodes in the received messages inmore than 5, the processing resources of the Node Processor growrapidly, by (depth−1)! The optimum depth may vary based on differentproblem constraints.

Both the Message Handler and the Stop Processor see this message on theAdministration Bus. The Message Handler and Stop Processor work togetherto update the pointer if needed and then the Message Handler inserts theupdated message in rank-ordered sequence with other messages in itsstack of messages.

The Message Handler does not place any messages on the Node Bus untilall Node Processors have sent any messages they need to send to theMessage Handler via the Administration Bus as indicated by the togglecounter. When the Message Handler's toggle counter accumulates up to thecount of nodes in the graph of all nodes, the Message Handler knows thatall Node Processors have provided whatever messages they have based onthe last message placed on the Node Bus. After a final check with theStop Processor for a pointer update (discussed below) the next messageis placed on the Node Bus by the Message Handler.

The creation of new messages by Node Processors are caused by priormessages received from the Node Bus. Unless terminated (pruned), eachmessage iteratively moves between Node Processors and the MessageHandler while its travel cost and node mask evolve. The Stop Processorkeeps checking for complete node masks, but during processing keepscreating new pointers to new travel paths as required. For example,there may be an existing pointer “X” to a path BCDEF stored on the StopProcessor. The Stop Processor then sees a message on the AdministrationBus that includes pointer X. The message also has a new node ID added,such as . . . CDEFT. The Stop Processor compares the last node ID ofpointer X (stored on the Stop Processor) with the second to last node IDof the message . . . CDEFT. If they are the same, then the currentmessage contains the first extension beyond path . . . BCDEF. If T isthe first extension beyond . . . BCDEF, then the updated path cancontinue to use pointer X whose path sequence will be appended with T,stored on the Stop Processor. In this case, there is no need for theStop Processor to inform the Message Handler to update the pointer andthe Message Handler can simply insert the message into its stack foreventual placement on the Node Bus. Suppose another message is obtainedwith the same pointer X, but for path . . . CDEFM. This means that asingle message placed on the Node Bus caused more than one NodeProcessor to generate a new message. Since the last node ID of pointer X(which is now T) is not the same as the second to last node ID in thenew message (which is F), the Stop Processor can generate a new pointer,copy pointer X to it and correct the last visited node, removing T andappending M. Then the Stop Processor must inform the Message Handler viathe Pointer Bus that the pointer in this message must be updated. Beforethe Message Handler places any message on the Node Bus, it must eitherget a message from the Stop Processor indicating either “no pointerupdate” or “pointer update”. This is required to ensure a messagedoesn't get placed on the Node Bus with the wrong pointer.

The path processing can progress only as fast as the Message Handlerplaces messages on the Node Bus which has a maximum communicationbandwidth. Similarly, the Message Handler can place messages onto anyone of several Node Buses to increase maximum handling speed. If thisarchitecture is used, it is imperative for every Node Processor to beable to simultaneously listen to every Node Bus. When the MessageHandler has no remaining messages in its message stacks, it sends a “nomore messages” message on the Node Bus. With this message, the NodeProcessors can stop all processing. When the Stop Processor hears thismessage, it can deliver to the Administration Bus the best current pathinformation (cost and node visitation sequence). The node visitationsequence is retrieved from memory on the Stop Processor using thepointer associated with the message demonstrating the lowest completetotal path cost, being the target path.

FIGS. 2N and 2Y show an example of three nodes between the Start Nodeand the Stop Node in the traveling salesman problem. The locations ofnodes are depicted in the shaded area along with the computed distancesbetween them. Below the shaded area, is shown what each processor isdoing after the initial start message is sent. Because there are noneighbor constraints specified, each Node Processor must respond tomessages originating from all nodes, add an increment of travel time andthen submit the new message to the Message Handler. For this example,the updates of node masks and pointers are omitted for simplicity. TheMessage Handler deposits the messages onto the Node Bus in increasingtemporal order where they can be further processed by more NodeProcessors. Three shaded cells in the spreadsheet, show where NodeProcessors detects that a prior node path with exactly the same nodevisits has a shorter time than a prior observation, so no message issent to the Message Handler. This is the pruning action described above.

The Stop Processor takes no action until it sees a full complement ofvisited nodes. Even then it must add-in the time from the last visitednode to the location of Stop Node. Even if a first complete node mask isobserved, there is still a possibility that another complete message,arriving later, could have a lower total oath time if it has a lowerfinal time to the Stop Node. Therefore, the Stop Processor must wait forone of two things to occur to be certain there are no shorter completesolutions. Either the Message Handler must announce that there are nomore messages to inspect (in which case the Stop Processor uses itscurrent shortest complete path) or the Stop Processor waits for theMessage Handler to place a message onto the Node Bus having a timegreater than that of the current shortest complete path (in which caseit also delivers the current shortest complete path). For this secondcase, if the Stop Processor were to add any non-zero time to the time(or cost) in the received message for the final travel to the Stop Node,the time or cost could only increase. If the time or cost is alreadyhigher than that of the shortest current complete path, then it is notpossible to have any subsequent complete solutions with lower time orcost. Either way, it is not possible for there to be a shorter path onceone of these two events has occurred. This is due to the temporal flowcharacteristic of the apparatus. In this simple example, only threepaths have been pruned and yet the total number of additions andcomparisons have been reduced. Using classical solution methods, findingthe shortest path requires 24 additions and 6 comparisons. Thissimplified example requires 15 additions and 9 comparisons. The savingsin computation increase rapidly as the number of nodes increases.

The example in FIGS. 2O and 2Z show what happens with four nodes betweenthe Start Node and the Stop Node. Following the same methodology, onecan see that the number of shaded cells (indicating a shorter path hasbeen observed by a Node Processor and to not send a message) hasincreased greatly. The larger group of nodes grows the complexity, butthe number of branches being pruned is also growing quickly. All of therows with shaded cells on the far left would not normally exist, due tomessage termination (pruning), when the embodiment is executing. Theyare only shown to indicate processing that can never occur because themessage on the far left cannot be placed onto the Node Bus by theMessage Handler. The shaded cells with text in the processor columns dohave to be computed and compared with prior messages in order to assertthat the message is not to be sent to the Message Handler, so there is aNode Processor processing cost to these, but not a bandwidth orsubsequent computational cost. In this example, there is a firstinstance of a complete message at t=24.6, but once the time going fromthe last node to the Stop Node is included, the final time is 35.91.This cannot be declared the lowest time solution until either theMessage Handler either declares no more messages in its stack or thetime present in any subsequent message on the message bus exceeds 35.91,and no other complete path with total time less than 35.91 is found.Almost immediately after finding the first complete path, we showanother complete path at t=25.79 having a final time (including time forthe final travel leg to the Stop Node) of 32.6 which eventually turnsout to be the lowest complete path time. At time 32.6, no more messageshave been observed with complete visitation paths, so the Stop Processorsends a “stop processing” command on the Node Bus. The AdministrationProcessor then receives a message from the Stop Processor which includesthe final time and node visitation sequence for the target path.

The computation cost of this four-node example again shows the benefitof the apparatus. Classical methods take 24 compares and 120 additionswhile this embodiment accomplishes the job in 42 compares and 53additions. The historical method for a five node embodiment requires 120compares and 720 additions where this embodiment finds the result in 143compares and 168 additions. With more nodes, the gap in computation costdiverges exponentially from the classical methods. Just to see how theproblem normally grows as adding nodes 6, 7, and 8 . . . total comparesincreases to 720, 5040, and 40320 while count of additions increases to5040, 40320, and 362880 respectively. When considering problems withhundreds or thousands of nodes, the quantity of required calculationsrapidly exceeds worldwide computational resources. Since the number ofpossible paths increases by n! assume having a 1000 node problemrequiring a large data center of servers to solve the problem withintime T. If the size of the problem increases by just one node, there isthen need 1001 data centers to solve the problem. Just one more nodemight require more data centers than are available in the world. Ifprune 119 out of every 120 paths are pruned (looking at the last fivenodes) and such pruning occurs at every Node Processor at every step ofprocessing, the total requirement for processing is reduced drastically.

There are many practical applications for the embodiments describedherein that can use the ability to terminate processing shortly after afirst solution is found, the ability to vigorously prune calculationbranches with crowd processing, and use scalable, high bandwidthcommunication buses. Some applications include genetic engineering,cryptography, linear programming, systems optimization, graphtheoretical problems, complex systems modeling and numerical methods.

In one or more embodiments, all of the nodes (graph) in an exacttraveling salesman problem can be visited by any of the other nodes,irrespective of cost, distance or time between them. It makes sense thattransiting between nodes on opposite sides of the graph (themultidimensional space containing the nodes) is likely to incur a highercost than transiting between nodes in the immediate vicinity of eachother. This however is not guaranteed.

Some algorithms can group nodes within a graph having relatively closeproximity to each other (closer than the average distance between alladjacent nodes in the graph). A graph of nodes may have multiple groupsand neighbor relationships must be made between at least one pair ofnodes where there is one node in each of two groups to be connected.Some of the difficulties in classical graph theory algorithms fordetermining these groups is whether the group's encompassing contourshould be “round” or whether they can be encompassed by complex shapes.Constraints on the shape of a group's encompassing contour lead to evenmore complex theories regarding the ability to ensure “complete graphconnectivity” (all nodes can be visited between starting and endingpoints).

One or more embodiments can include a unique mode of operation andcapability to ensure complete graph connectivity. To test for completegraph connectivity, the Message Handler (knowing which node is the StartNode, as informed by the Administration Processor) drops a “start”message onto the Node Bus. This message is heard by all Node Processorsconnected to the bus. In this mode of operation, each node that is aneighbor (defined as having a predetermined cost of travel betweennodes) of the Start Node sets its own flag, indicating it has somethingto report to the Message Handler. In sequence, using the node ID, eachof these neighbor Node Processors reports to the Message Handler via theAdministration Bus, that it is a neighbor of the node sourcing themessage observed on the Node Bus (in this case, the Start Node) alongwith the cost between the nodes. The Message Handler is able to collectthe list of all nodes which are neighbors of the Start Node. Such a listcan be called a “start neighbor list.” The Message Handler haspreviously received the full set of nodes in the graph from theAdministration Processor. By subtraction the Message Handler determineswhich nodes are missing from “start neighbor list.” For instance, ifthere are 112 nodes in the graph and 54 are in the “start neighborlist”, then 58 nodes are “unconnected” because they are not neighbors ofthe Start Node. The Message Handler rank-orders the “start neighborlist” based on reported cost from lowest to highest. If complete graphconnectivity has not been established (evidenced by no missing nodes),the Message Handler drops another message onto the Node Buscorresponding to the nearest (lowest cost) neighbor of the Start Node,being the first neighbor in the “start neighbor list.” In this mode ofoperation, all nodes that have previously responded to the MessageHandler are disabled and can send no more messages to the MessageHandler. When this next message is dropped onto the Node Bus, anyadditional nodes that are neighbors of the sourcing node (on behalf ofwhich the message is sent by the Message Handler) send theirconsequential messages to the Message Handler (assuming they have notbeen disabled). This set of responses is given a new name which isdesignated “start neighbor list 1” which means it is the neighbor listassociated with the first node in the “start neighbor list”. The MessageHandler again checks for graph connectivity completeness and if notfound, the Message Handler drops another message onto the Node Bus fromthe second member of the list “start neighbor list.” Again, the MessageHandler receives responses from the Node Processors and creates anotherlist called “start neighbor list 2.” Each Node Processor that provides amessage to the Message Handler is disabled from subsequent processing.This process repeats using messages from “start neighbor list” until theMessage Handler finds complete graph connectivity. If complete graphconnectivity is not found by the end of all messages in “start neighborlist”, the Message Handler has to extend the search by dropping amessage onto the Node Bus corresponding to the first listed entry of“start neighbor list 1.” Responses to this message create another listcalled “start neighbor list 1, 1.” During the search process, this canbe extended to “start neighbor list 1, N” where N is the number oflisted neighbors in the “start neighbor list 1.” Perhaps there is nopath to graph completeness, irrespective of how many layers deep thisprocess goes. Note that as processing down these many paths andsub-paths progresses, the remaining unconnected node lists get smaller.Again, this is because each time any node reports to the MessageHandler, it is permanently removed from sending any more messages to theMessage Handler. In another example, assume an extended node list called“start neighbor list 2, 4, 8, 2, 1, 1, 7, 9, 11.” This means that thestart message was sent, resulting in a list of unconnected nodes called“start neighbor list.” Then a message for the second of these nodesresulted in another list call “start neighbor list 2.” A message for thefourth member of that list caused a list “start neighbor list 2, 4” tobe generated. The remaining sequential lists resulted from dropping theeighth, second, first, first, seventh, ninth, and eleventh entries inthe resulting lists respectively. If any message is dropped onto theNode Bus by the Message Handler without any Node Processor responses,the Message Handler simply moves to the next message. If after searchingall possible paths for complete graph connectivity, the Message Handlercannot find it, the Message Handler informs the Administration Processoraccordingly and the Administration Processor returns a message back to aclient computer system such as “error, graph connectivity incomplete.”Without graph connectivity, it is not possible to find any solution tothe traveling salesman problem.

With a large number of nodes, the cascading of these visited neighborlists while testing for any complete path can become computationallyexpensive, but still much less than the computational cost to find thetarget path. In the absence of any complete path, we can avoid thecomputational cost of finding the target path. Recall that if there areno neighbor constraints between nodes, there cannot be any strandedislands of nodes and complete graph connectivity is guaranteed. Eachsubsequent response list gets smaller as the search for graphcompleteness progresses, so even though the total number of lists maygrow rapidly, this is partially mitigated by rapidly reducing counts ofunconnected nodes. Further optimization of checking complete graphconnectivity may be accomplished by treating all nodes within a nodegroup as a node cluster. A requirement of this approach is that allnodes within a node cluster must have connectivity to all other nodes inthe node cluster. Any neighbor of any node within the node cluster isthen considered a neighbor of the node cluster. Once this is completed,the node cluster behaves computationally like a single node with a lotof neighbors. Some embodiments can test for complete graph connectivitybetween nodes and nodes clusters, which requires less processing.

Once an embodiment ensures complete graph connectivity, its mode ofoperation changes to searching for the target path. Processingreduction/optimization using graph clusters to produce node groupscannot guarantee a “complete” solution to the traveling salesmanproblem, but can present an acceptable tradeoff between processing costand exactness of the solution.

FIG. 2P depicts an illustrative embodiment of a method 260 in accordancewith various aspects described herein. In one or more embodiments, themethod 260 can be implemented by a server, computing device, or anyother processing system. The method 260 can include iterativelyproviding, from a Message Handler of a processing system, messages toeach of a group of Node Processors of the processing system. Each of thegroup of Node Processors represents a node or a group of nodes.

The method 260 can include, at 262, providing, by the Message Handler toa Node Bus, a group of first messages. Each first message includes acost associated with a path of nodes visited by each first message.Further, the method 260 can include, at 264, determining, by each of thegroup of Node Processors, paths having common endpoints among a portionof the group of first messages. In addition, the method 260 can includethe processing system, at 266, identifying, by each of the group of NodeProcessors, a cost for each of the paths having common endpointsresulting in a group of common endpoint costs. Also, the method 260, at268, identifying, by each of the group of Node Processors, a lowest costfrom among the group of common endpoint costs. Further, the method 260can include, at 270, identifying, by each of the group of NodeProcessors, a selected path associated with the lowest cost. A nextgroup of messages includes the selected path. The iteratively providingof the messages results and comparison of travel costs between pathshaving common endpoints, provides for pruning of a majority of paths,leaving permissible paths for continued processing. If a target path isnot found, the method 260 can include the recursive processing step 272,providing a next group of messages to be processed for extension of aselected path. In addition, the method 260, determines by processingstep 274, a target path which is the final permissible path afterpruning of all other paths for having higher costs.

While for purposes of simplicity of explanation, the respectiveprocesses are shown and described as a series of blocks in FIG. 2P, itis to be understood and appreciated that the claimed subject matter isnot limited by the order of the blocks, as some blocks may occur indifferent orders and/or concurrently with other blocks from what isdepicted and described herein. Moreover, not all illustrated blocks maybe required to implement the methods described herein.

In one or more embodiments, the target path will be a complete path, acomplete shortest path, and/or a most efficient path. If every node inthe graph of nodes is permitted to be a neighbor of every other node,then the target path will also provide an exact solution, otherwise itwill provide an approximate solution. The pruning of paths allows theprocessing system to only use the remaining paths to find/calculate thetarget path and forego using terminated/pruned paths to find/calculatethe target path, thereby improving the efficiency in finding/calculatingthe target path by the processing system.

In one or more embodiments, the lowest cost of a path is associated witha first path from the common paths. Further, in method 260, identifyingthe lowest cost from among the costs of a group of paths having commonendpoints can comprise identifying a next higher cost from among thesecosts. The next higher cost is associated with a second path from thecommon paths, comparing the lowest cost to the next higher cost, anddetermining the lowest cost is lower than the next highest cost. Thecost of any path can be one of time, distance, available bandwidth,latency, or throughput.

In one or more embodiments, a method can comprise a processing systemobtaining, by a Message Handler of a processing system, an initiationmessage, wherein the initiation message identifies an initial cost and aStart Node visited. Further, the method can comprise the processingsystem providing, by the Message Handler, the initiation message on acommunication bus of the processing system, In addition, the method cancomprise the processing system receiving, by the Message Handler, afirst group of messages from a group of computing threads that eachrepresent a different one of a group of nodes. Each of the first groupof messages includes first costs and first nodes visited. Each of thefirst costs and each of the first nodes visited are associated with acorresponding one of the group of nodes. The receiving of the firstgroup of messages is responsive to the providing of the initiationmessage on the communication bus. Also, the method can include theprocessing system providing, by the Message Handler, the first group ofmessages on the communication bus according to a first order that isbased on the first costs. Further, the method can include the processingsystem receiving, by the Message Handler, a second group of messagesfrom a first subset of the group of computing threads. Each of thesecond group of messages includes second costs and second nodes visited.Each of the second costs and each of the second nodes visited areassociated with a corresponding one of the first subset of the group ofnodes. The receiving of the second group of messages is responsive tothe providing of one of the first group of messages on the communicationbus. In addition, the method can include the processing systemproviding, by the Message Handler, the second group of messages on thecommunication bus according to a second order that is based on thesecond costs. Also, the method can include the processing systemreceiving, by the Message Handler, a third group of messages from asecond subset of the group of threads. Each of the third group ofmessages includes third costs and third nodes visited. Each of the thirdcosts and each of the third nodes visited are associated with acorresponding one of the second subset of the group of nodes. Thereceiving of the third group of messages is responsive to the providingof one of the second group of messages on the communication bus.Further, the method can include the processing system providing, by theMessage Handler, the third group of messages on the communication busaccording to a third order that is based on the third costs. At leastone of the group of computing threads determines a lower cost associatedwith the third nodes visited and does not generate a message that ispart of the third group of messages based on the lower cost beingdetermined. The method can include the processing system stopping amessage being placed on the communication bus if the cost associatedwith the message is greater than a total cost for another message thatindicates all of the same nodes have been visited with the same commonendpoints. The group of computing threads can be part of the processingsystem. The Message Handler and group of computing threads can be partof a distributed computing environment.

FIGS. 2Q-2U are block diagrams and associated paths illustrating anexample, non-limiting embodiment of a system functioning within thecommunication network of FIG. 1 in accordance with various aspectsdescribed herein.

Referring to FIG. 2Q, in one or embodiments, FIG. 2Q illustrates aconcept of pruning paths in calculating a target path (that can be apath that traverses each and every node i.e., complete path or a paththat traverses each and every node with the lowest cost i.e., completeshortest path). Pruning can include discarding intermediate paths thatmay be costlier than less costly intermediate paths. The system 200 acomprises group of nodes 202 a-218 a (i.e. network of nodes) that caninclude a source node 202 a, all of which are interconnected to eachother with links. Each link can be associated with a cost. In furtherembodiments, the group of nodes 202 a-218 b may be processors (i.e.,Node Processors) in a computing/processing environment including a cloudcomputing environment and/or virtual computing environment. Inadditional embodiments, the group of nodes 202 a-218 a may be networkelements in a communication network. The group of nodes 202 a-218 a canbe a network of nodes or a collection of nodes each of which implementfunctions (some of which may be the same).

In one or more embodiments, each node can be a Node Processor within acomputing environment. Any Node Processor can receive a messageoriginating from another Node Processor and having an accumulated costfrom the totality of node travels up to the other node which originatesthe message. The current Node Processor adds to the prior accumulatedcost, the cost of travel between the node originating the message andthe current node. Further, the Node Processor may request a MessageHandler to drop a message onto a communication bus of the computingenvironment, receivable by other Node Processors in the computingenvironment. In this embodiment, Node Processors do not directlycommunicate with one another, but instead via a Message Handler thatcoordinates message flows on a common communication bus. For example,node A 204 a can receive several messages. A first message can bereceived directly from the source node A 204 a at a cost of 3. Inresponse to receiving the first message, node A 204 a can forward amessage to a communication bus that is received by node B 206 a withaccumulated cost of 8 and node D 210 a with accumulated cost of 9, andforward a message to the communication bus that is received by node C208 a with accumulated cost of 13. A second message received by node A204 a can be from the source node 202 through node B 206 a at anaccumulated cost of 6. In response to receiving the second message, nodeA 204 a can provide a message to node D 210 a with cost 12 and provideanother message to node C 208 a with an accumulated cost 16. Note, nomessage is sent from node A 204 a to the source node 202 a or to node B206 a, as message son the path already visited these nodes. The messagetraveling between nodes carries a history of node visitations and thesource node 202 a, being part of the travel history.

In one or more embodiments, two different types of methods can be usedto compute a target path traversing each and every node in system 200 a,which are related to each other. One method can be called the greedypath method while the other method can be called the cost statistics andsequestration method. Both are iterative methods in which each iterationcomputes the cost of partial paths of a target path and determines theknown minimum solution (KMS) for each iteration, which is the partialpath having the least cost for a particular iteration (Note, in one ormore embodiments, the KMS can take into account some othercriterion/factor/variable and may not be the minimum cost solution butrather the lowest solution that satisfies the othercriterion/factor/variable, which may end up being the second or thirdlowest cost solution overall without considering the othercriterion/factor/variable, for example). Both iterative methods attemptto balance of finding a low-cost target path with the number ofcalculations needed to find such a low-cost path. As the number of nodeslinearly increase in systems 200 a, the number of calculations to find alow-cost target path exponentially increase. Users of the method to findlow-cost target paths may have processing constraints that limit thenumber of calculations a system can perform. Thus, the iterative methodssuch as the greedy path method and the cost statistics and sequestrationmethod strike a balance in finding a low-cost target path in view ofprocessing constraints.

Referring to FIG. 2R, in one or more embodiments, implementing thegreedy path method, in a first iteration, the source node 202 a sends amessage to each of node A 204 a, node B 206 a, and node C, 208 aresulting in the following associated paths/costs: S-A=3; S-B=1; andS-C=2. Based on these paths and their associated costs, the KMS=1 forthe path S-B. In the second iteration, paths S-A and S-C are discarded(i.e., further messages are not sent along paths S-A and S-C becausethey have costs that are higher than the KMS), but messages are sentalong path S-B resulting the following associated paths/costs: S-B-A=6,S-B-C=4, and S-B-E=5. Based on these paths and their associated costs,the KMS=4. In the third iteration, paths S-B-E and S-B-A are discarded,and messages are sent along path S-B-C resulting in the followingassociated paths/costs: S-B-C-A=14; and S-B-C-F=13. Based on these pathsand their associated costs, the KMS=13 for the path S-B-C-F. In thefourth iteration, path S-B-C-A is discarded, and messages are sent alongpath S-B-C-F resulting in the following associated paths/costs:S-B-C-F-E=21 and S-B-C-F-D=25. Based on these paths and their associatedcosts, the KMS=21. In the fifth iteration, the path S-B-C-F-D isdiscarded, and messages are sent along the path S-B-C-F-E resulting inthe following associated path/cost, S-B-C-F-E-D=31. Based on this pathand its associated cost, the KMS=31 for the path S-B-C-F-E-D=31. In thesixth iteration, messages are sent along path S-B-C-F-E-D resulting inthe following associated path/cost, S-B-C-F-E-D-A=37. This pathtraverses each and every node in system 200 a and hence can bedesignated as a target path. However, the cost of this target path maynot be lower than utilizing the cost statistics and sequestrationmethod.

Referring to FIG. 2S, in one or more embodiments, implementing the coststatistics and sequestration method, the cost statistics for the networkshown in system 200 a include the average cost=5.3 and the standarddeviation=2.7. Based on the KMS and the cost statistics, some paths withcosts above a standard deviation can be sequestered to a sequestrationhandler (e.g., a separate processor in system 200 a, similar in functionto the message handler) to be calculated later, if need be to find apath with a lower cost that traverses each node. In a first iteration, amessage can be sent from the source node to each of the adjacent nodesnode A 204 a, node B 206 a, and node C 208 a resulting in the followingassociated paths/costs: S-A=3; S-B=1; and S-C=2. Based on these pathsand their associated costs, the KMS=1. Further, the cost of each path iswithin the average cost (5.3) such that in a second iteration, no pathsare sequestered and messages are sent along paths S-A, S-B, and S-C,resulting in the following associated paths/costs: S-B-A=6; S-B-C=4;S-B-E=5; S-C-A=12; S-C-B=5; S-C-F=11; S-A-B=8; S-A-C=13; and S-A-D=9.Based on these paths and their associated costs, the KMS=4 associatedwith path S-B-C. Further, the cost associated with path S-B=1, and withaverage cost=5.3 and standard deviation=2.7, any path with an associatedcost in the second iteration greater than 9 (average cost (5.3) inaddition to one standard deviation (2.7)) in addition to the KMS) can besequestered, resulting in paths S-C-A, S-C-F, and S-A-C beingsequestered. These paths are sequestered because it is unlikely than anypaths S-C-A, S-C-F, and S-A-C would result in being a target path with alower cost than a target path that includes S-B-C, S-B-E, S-C-B, S-B-A,S-A-B, and S-A-D based on the cost statistics (e.g., average cost andstandard deviation). The cost associated with paths S-C-A=12 andS-C-F=11 is between one standard deviation and two standard deviationssuch that they are sequestered in a first sequestration bucket. The costassociated with path S-A-C=13 is between two standard deviations andthree standard deviations such that it is sequestered in a secondsequestration bucket. In a third iteration, messages are sent alongpaths S-B-C, S-B-E, S-C-B, S-B-A, S-A-B, and S-A-D, resulting in thefollowing associated paths/costs: S-B-C-A=14, S-B-C-F=13, S-B-E-D=15,S-B-E-F=13, S-C-B-A=10, S-C-B-E=9, S-B-A-C=16, S-B-A-D=12, S-A-B-C=11,S-A-B-E=12, S-A-D-E=19, and S-A-D-F=21. Based on these paths and theirassociated costs, the KMS=9 associated with path S-C-B-E. Further, thecost associated with path S-B-C=4, and with average cost=5.3 andstandard deviation=2.7, any path with an associated cost in the thirditeration greater than 12 (average cost (5.3) in addition to onestandard deviation (2.7) in addition to the KMS) can be sequestered,resulting in paths S-B-C-A, S-B-C-F, S-B-E-D, S-B-E-F, S-B-A-C, S-A-D-E,S-A-D-F being sequestered. The cost associated with paths S-B-C-A=14,S-B-C-F=13, S-B-E-D=15, S-B-E-F=13 is between one standard deviation andtwo standard deviation such that they are sequestered in the firstsequestration bucket. The cost associated with path S-B-A-C=16 isbetween two standard deviations and three standard deviations such thatit is sequestered in a second sequestration bucket. The cost associatedwith path S-A-D-E=19 is between three standard deviations and fourstandard deviations such that it is sequestered in a third sequestrationbucket. The cost associated with path S-A-D-F=21 is between fourstandard deviations and five standard deviations such that it issequestered in a fourth sequestration bucket. In a fourth iteration,messages are sent along paths S-C-B-E, S-C-B-A, S-A-B-C, S-B-A-D,S-A-B-E, resulting in the following associated paths/costs:S-C-B-E-D=19, S-C-B-E-F=17, S-C-B-A-D=16, S-A-B-C-F=20, S-B-A-D-E=22,S-B-A-D-F=24, S-A-B-E-D=22, and S-A-B-E-F=20. Based on these paths andtheir associated costs, the KMS=16 associated with path S-C-B-A-D.Further, the cost associated with path S-C-B-E=9, and with averagecost=5.3 and standard deviation=2.7, any path with an associated cost inthe fourth iteration greater than 17 (average cost (5.3) in addition toone standard deviation (2.7) in addition to the KMS) can be sequestered,resulting in paths S-C-B-E-D, S-A-B-C-F, S-B-A-D-E, S-B-A-D-F,S-A-B-E-D, S-A-B-E-F being sequestered. The cost associated with pathsS-C-B-E-D=19, S-A-B-C-F=20, and S-A-B-E-F=20 is between one standarddeviation and two standard deviations such that they are sequestered inthe first sequestration bucket. The cost associated with paths S-B-A-D-Eand S-A-B-E-D are between two standard deviations and three standarddeviations such that they are sequestered in a second sequestrationbucket. The cost associated with path S-B-A-D-F=24 is between threestandard deviations and four standard deviations such that they aresequestered in a third sequestration bucket. In a fifth iteration,messages are sent along paths S-C-B-A-D, and S-C-B-E-F, resulting in thefollowing associated paths/costs: S-C-B-A-D-E=26, S-C-B-A-D-F=28, andS-C-B-E-F-D=29. Based on these paths and their associated costs, theKMS=26 associated with path S-C-B-A-D-E. Further, the cost associatedwith path S-C-B-A-D=16, and with average cost=5.3 and standarddeviation=2.7, any path with an associated cost in the fifth iterationgreater than 24 (average cost (5.3) in addition to one standarddeviation (2.7) in addition to the KMS) can be sequestered, resulting inpaths S-C-B-A-D-F and S-C-D-E-F-D being sequestered. The cost associatedwith paths S-C-B-A-D-F=28 and S-C-D-E-F-D=29 is within two standarddeviations and three standard deviations such that it is sequestered inthe second sequestration bucket. In a sixth iteration, messages are sentalong path S-C-B-A-D-E, resulting in the following associated path/cost:S-C-B-A-D-E-F=34. The path S-C-B-A-D-E-F has traversed each and everynode in system 200 a such the calculation of a target path has beendetermined. The target path is S-C-B-A-D-E-F and is associated with acost of 34.

Referring to FIG. 2R and FIG. 2S, in one or more embodiments, comparingthe cost of the target path determined in FIG. 2R utilizing the greedypath method (37) with the cost of the target path determined in FIG. 2Sutilizing the cost statistics and sequestration method (34) shows thecost statistics and sequestration method allows a target path with alower cost to be determined. However, the greedy path method reveals acost of the target path that is close to the cost of the target pathdetermined by the cost statistics and sequestration method but computesless calculations (e.g., 12 calculations utilizing the greedy pathmethod compared to 36 calculations utilizing the cost statistics andsequestration method). A user can determine whether it is worth thehigher number of calculations, 36 vs. 12, to achieve the lower cost, 34vs. 37.

Referring to FIG. 2T, in one or more embodiments, paths that have beensequestered during the iterative cost statistics and sequestrationmethod associated with FIG. 2S are shown. Referring to FIG. 2U, in someembodiments, the cost statistics and sequestration method can continueby computing target paths for the sequestered paths. The cost statisticsand sequestration method can continue by first calculating costs targetpaths of paths sequestered from the most recent iteration and with thelowest ranked bucket. Paths that are sequestered most recently may bemore likely to lead to finding a target path that has a lower cost thanthe target path found in FIG. 2S. Thus, FIG. 2U illustrates firstcalculating target paths for the second sequestration bucket from thefifth iteration. In the sixth iteration, the resulting paths/costs are:S-C-B-A-D-F-E=36; and S-C-B-E-F-D-A=35. These paths can be target pathsas each path traverses each and every node in system 200 a.

In one or more embodiments, the cost statistics and sequestration methodcan continue to the next sequestration bucket within the iteration, ifany, or continue to the lowest sequestration bucket in the previousiteration. Thus, the target path to be calculated are the pathssequestered from the first sequestration bucket from the fourthiteration. In the fifth iteration, the resulting paths/costs are:S-C-B-E-D-A=25; S-C-B-E-D-F=31; S-A-B-C-F-D=32; S-A-B-C-F-E=28;S-A-B-E-F-C=29; and S-A-B-E-F-D=32. Based on these paths/costs, in thesixth iteration the resulting paths/costs are: S-A-B-C-F-E-D=38; andS-A-B-C-F-C-E=39. Note, that there can be other paths such asS-C-B-E-D-F-C, however, the path traverses a node twice (node C 208 a)before reaching a node it has yet to traverse (node A 204 a) and is notincluded in the chart 235 a.

In one or more embodiments, the resulting costs of the target paths,S-C-B-A-D-F-E=36, S-C-B-E-F-D-A=35, S-A-B-C-F-E-D=38, andS-A-B-C-F-C-E=39 are more than the cost found of the target pathcalculated in FIG. 2S, S-C-B-A-D-E-F=34. Based on the costs of theresulting target paths that traverse each and every node of system 200a, further target paths can be calculated from the paths in thesequestration buckets. Users of the cost statistics and sequestrationmethod can balance the trade-off between implementing more calculations(e.g., processing power) with the current lowest cost of a target pathto determine whether it is worth expending further processing power incalculating target paths from the paths in the sequestration bucket withthe hope to finding a new target path with a lower cost thanS-C-B-A-D-E-F=34. As can be seen in chart 235 a, the costs of targetpaths found from the sequestered paths that include S-C-B-E-F-D-A=35,S-C-B-A-D-F-E=36, S-A-B-C-F-E-D=38, and S-A-B-C-F-D-E=42, all of havecosts higher than the target path found in FIG. 2S, S-C-B-A-D-E-F=34.

FIGS. 2V-2X depict illustrative embodiments of methods in accordancewith various aspects described herein. Referring to FIG. 2Q and FIG. 2V,in one or more embodiments, method 260 a can implemented by a messagehandler that is part of the systems 200 a. The method 260 a canimplement aspects of the greedy path method described herein. Further,the method 260 a can include the message handler, at 262 a, providing amessage to each of a group of node processors of system 200 a resultingin a group of messages. Additionally, the method 260 a can include themessage handler, at 264 a, determining a cost associated with a path ofeach message resulting in a group of costs and a group of paths. Inaddition, the method 260 a can include the message handler, at 266 a,identifying a known minimum solution (KMS), wherein the KMS is a leastcost from the group of costs. Also, the method 260 a can include themessage handler, at 268 a, selecting at least one path from the group ofpaths associated with the KMS resulting in at least one selected path.Further, the method 260 a can include the message handler, at 272 a,determining whether a selected path is a target path (a path thattraverses each and every node). If a target path is not determined, thenthe method 260 a returns to the message handler, at 262 a, providing agroup of next messages and the method 260 a continues iteratively untila target path is determined. Once a target path is determined at 272 a,the method 260 a stops when the message handler determines, at 274 a,the target path traverses each and every node with the lowest cost.

Referring to FIGS. 2Q and 2W, in one or more embodiments, method 275 acan implemented by a message handler that is part of the systems 200 a.The method 275 a can implement aspects of the cost statistics andsequestration method described herein. Further, the method 275 a caninclude the message handler, at 276 a, determining, cost statistics ofthe nodes in system 200 a, which includes determining an average costbetween any two nodes of the group of nodes, and determining a standarddeviation associated with the average cost. Additionally, the method 275a can include the message handler, at 278 s, providing a group ofmessages to each of a group of node processors. In addition, the method275 a can include the message handler, at 280 a, determining a costassociated with a path of each message resulting in a group of costs anda group of paths. Also, the method 275 a can include the messagehandler, at 286 a, identifying a known minimum solution (KMS). The KMSis the least cost from the group of costs. Further, the method 275 a caninclude the message handler, at 288 a, selecting at least one path fromthe group of paths associated with the KMS according to the average costand the standard deviation resulting in at least one selected path. Inaddition, the method 275 a can include the message handler, at 289 a,sequestering unselected paths based on the average cost and the standarddeviation (as described herein). Also, the method 275 a can include themessage handler, at 290 a, can determine whether the any selected pathis a target path (a path that traverses each and every node). If atarget path is not determined, then the method 275 a returns toproviding, at 276 a, a group of next messages and the method 260 acontinues iteratively until a target path is determined. Once a targetpath is determined at 290 a, the method 292 a stops when the messagehandler determines, at 292 a, the target path traverses each and everynode with the lowest cost.

Referring to FIG. 2Q and FIG. 2X, in one or more embodiments, method 265b be implemented by a user after method 275 a to determine whether alower cost target path can be found from the sequestered paths. Method265 b implements aspects of the cost statistics and sequestration methoddescribed herein. Moreover, method 265 b can be implemented by one ormore sequestration handlers (a processor dedicated to implementingmethod 265 b) on paths sequestered in a most recent iteration indifferent sequestration buckets (e.g., first sequestration bucket aresequestered paths that have costs within one standard deviation and twostandard deviations of the average cost, second sequestration bucket aresequestered paths that have costs within two standard deviations andthree standard deviations of the average cost, etc.). Further, themethod 265 b can include a sequestration handler, at 262 b, providing agroup of messages to each of a group of node processors. In addition,the method 265 b can include the sequestration handler, at 264 b,determining a cost associated a path with each message resulting in agroup of costs and a group of paths. Also, the method can include thesequestration handler, at 266 b, identifying the KMS. The KMS is theleast cost from the group of costs. Further, the method 265 b caninclude the sequestration handler, at 268 b, selecting at least one pathfrom the group of paths associated with the KMS resulting in at leastone selected path. Also, the method 265 b can include the sequestrationhandler, at 272 b, can determine whether the any selected path is atarget path (a path that traverses each and every node). If a targetpath is not determined, then the method 265 b returns to providing, at262 b, a group of next messages and the method 265 b continuesiteratively until a target path is determined. Once a target path isdetermined at 272 b, the method 265 b stops when the sequestrationhandler, at 274 b, determines the target path traverses each and everynode with the lowest cost.

One or more embodiments can include a method comprising iterativelyproviding, from a message handler of a processing system including aprocessor, a first message to each of a group of node processors of theprocessing system resulting in a group of first messages, wherein eachof the group of node processors represents a node of a group of nodes,wherein the iteratively providing of the group of first messagescomprises: determining, by the message handler, a cost associated with apath of each first message resulting in a first group of costs and afirst group of paths; identifying, by the message handler, a knownminimum solution (KMS), the KMS is a least cost from the first group ofcosts; selecting, by the message handler, at least one path from thefirst group of paths associated with the KMS resulting in at least onefirst selected path; and providing, by the message handler, a nextmessage that includes the at least one first selected path and based onthe KMS to a first portion of the group of node processors of theprocessing system resulting in a first group of next messages and afirst plurality of selected paths The method further comprises,responsive to the iteratively providing of the group of first messagesand first group of next messages, determining, by the message handler, afirst target path that is a remaining path of the first plurality ofselected paths, the remaining path is identified from the iterativelyproviding of the group of first messages and the first group of nextmessages, and the first target path is through each node of the group ofnodes. Additionally, the method can comprise determining, by the messagehandler, an average cost between any two nodes of the group of nodes,and determining, by the message handler, a standard deviation associatedwith the average cost. Also, the method can include the selecting of theat least one path from the first group of paths comprises selecting, bythe message handler, the at least one path from the first group of pathsaccording to the average cost and the standard deviation. Further, themethod can comprise identifying, by the message handler, a first portionof the first group of paths such that each of the first portion of thefirst group of paths is associated with a first cost that is more thanthe average cost and the standard deviation associated with the averagecost resulting a group of sequestered selected paths and a firstidentification. In addition, the method can comprise providing, by themessage handler, the first identification of group of sequestered pathsto a sequestration handler, wherein the processing system comprises thesequestration handler.

The method can further comprise iteratively providing, from thesequestration handler, a second message to each of a second portion of agroup of node processors of the processing system resulting in a groupof second messages, the iteratively providing of the group of secondmessages comprises: determining, by the sequestration handler, a costassociated with a path of each second message resulting in a secondgroup of costs and a second group of paths; identifying, by thesequestration handler, the known minimum solution (KMS), the KMS is aleast cost from the second group of costs; selecting, by thesequestration handler, at least one path from the second group of pathsassociated with the KMS resulting in at least one second selected path;and providing, by the sequestration handler, a next message thatincludes the at least one second selected path and based on the KMS to athird portion of the group of node processors of the processing systemresulting in a second group of next messages and a second plurality ofselected paths. In addition, the method can comprise, responsive to theiteratively providing of the group of second messages and second groupof next messages, determining, by the sequestration handler, a secondtarget path that is a remaining path of the second plurality of selectedpaths, the remaining path is identified from the iteratively providingof the group of first messages and the second group of next messages,the second target path is through each node of the group of nodes. Themethod can include that a cost associated with the second target path islower than a cost associated with the first target path, the firstand/or second target path is a complete path, and the first and/orsecond target path is a complete shortest path. Further, the cost is oneof time, distance, monetary cost, available bandwidth, latency,throughput, risk, or probability of success.

One or more embodiments can include a device, comprising a processingsystem including a processor, a group of node processors, anadministration processor, and a message handler, each of the group ofnode processors represents a node of a group of nodes, and a memory thatstores executable instructions that, when executed by the processingsystem, facilitates performance of operations. The operations cancomprise determining, by the message handler, an average cost betweenany two nodes of the group of nodes, and determining, by the messagehandler, a standard deviation associated with the average cost. Further,the operations can comprise iteratively providing from the messagehandler of the processing system, a first message to each of the groupof node processors resulting in a group of first messages, theiteratively providing of the group of first messages comprises:determining, by the message handler, a cost associated with a path ofeach first message resulting in a first group of costs and a first groupof paths; identifying, by the message handler, a known minimum solution(KMS), the KMS is a least cost from the first group of costs; selecting,by the message handler, at least one path from the first group of pathsassociated with the KMS according to the average cost and the standarddeviation resulting in at least one first selected path; and providing,by the message handler, a next message that includes the at least onefirst selected path and based on the KMS, the average cost, and thestandard deviation to a first portion of the group of node processors ofthe processing system resulting in a first group of next messages and afirst plurality of selected paths. In addition, the operations cancomprise responsive to the iteratively providing of the group of firstmessages and the first group of next messages, determining, by themessage handler, a first target path that is a remaining path of thefirst plurality of selected paths, the remaining path is identified fromthe iteratively providing of the group of first messages and the firstgroup of next messages, and the first target path is through each nodeof the group of nodes.

The operations can further comprise identifying, by the message handler,a first portion of the group of paths such that each of the firstportion of the group of paths is associated with a first cost that ismore than the average cost and the standard deviation associated withthe average cost resulting a group of sequestered selected paths and afirst identification. Additionally, the operations can compriseproviding, by the message handler, the first identification of group ofsequestered paths to a sequestration handler, wherein the processingsystem comprises the sequestration handler.

The operations can also include iteratively providing, from thesequestration handler, a second message to each of a second portiongroup of node processors of the processing system resulting in a groupof second messages, the iteratively providing of the group of secondmessages comprises: determining, by the sequestration handler, a costassociated with a path of each second message resulting in a secondgroup of costs and a second group of paths; identifying, by thesequestration handler, the known minimum solution (KMS), the KMS is aleast cost from the second group of costs; selecting, by thesequestration handler, at least one path from the second group of pathsassociated with the KMS resulting in at least one second selected path;and providing, by the sequestration handler, a next message thatincludes the at least one second selected path and based on the KMS to athird portion of the group of node processors of the processing systemresulting in a second group of next messages and a second plurality ofselected paths. Also the operations can comprise responsive to theiteratively providing of the group of second messages and second groupof next messages, determining, by the sequestration handler, a secondtarget path that is a remaining path of the second plurality of selectedpaths, the remaining path is identified from the iteratively providingof the group of first messages and the second group of next messages,and the second target path is through each node of the group of nodes. Acost associated with the second target path is lower than a costassociated with the first target path

One or more embodiments can include a non-transitory, machine-readablemedium, comprising executable instructions that, when executed by aprocessing system including a processor, a group of node processors, anadministration processor, and a message handler, wherein each of thegroup of node processors represents a node of a group of nodes,facilitate performance of operations, the operations comprisingdetermining, by the message handler, an average cost between any twonodes of the group of nodes, and determining, by the message handler, astandard deviation associated with the average cost. Further, theoperations can comprise iteratively providing from the message handlerof the processing system, a first message to each of the group of nodeprocessors resulting in a group of first messages, the iterativelyproviding of the group of first messages comprises: determining, by themessage handler, a cost associated with a path of each first messageresulting in a group of costs and a group of paths; identifying, by themessage handler, a known minimum solution (KMS), wherein the KMS is aleast cost from the group of costs; selecting, by the message handler,at least one path from the group of paths associated with the KMSaccording to the average cost and the standard deviation resulting in atleast one selected path; and providing, by the message handler, a nextmessage that includes the at least one selected path and based on theKMS, the average cost, and the standard deviation to a portion of thegroup of node processors of the processing system resulting in a groupof next messages and a plurality of selected paths. In addition, theoperations can comprise responsive to the iteratively providing of thegroup of first messages and the group of next messages, determining, bythe message handler, a target path that is a remaining path of theplurality of selected paths, the remaining path is identified from theiteratively providing of the group of first messages and the group ofnext messages, and the target path is through each node of the group ofnodes. The target path can be a complete path and/or a complete shortestpath.

Referring now to FIG. 3 , a block diagram 300 is shown illustrating anexample, non-limiting embodiment of a virtualized communication networkin accordance with various aspects described herein. In particular avirtualized communication network is presented that can be used toimplement some or all of the subsystems and functions of communicationnetwork 100, the subsystems and functions of systems and implementmethods as described herein.

In particular, a cloud networking architecture is shown that leveragescloud technologies and supports rapid innovation and scalability via atransport layer 350, a virtualized network function cloud 325 and/or oneor more cloud computing environments 375. In various embodiments, thiscloud networking architecture is an open architecture that leveragesapplication programming interfaces (APIs); reduces complexity fromservices and operations; supports more nimble business models; andrapidly and seamlessly scales to meet evolving customer requirementsincluding traffic growth, diversity of traffic types, and diversity ofperformance and reliability expectations.

In contrast to traditional network elements—which are typicallyintegrated to perform a single function, the virtualized communicationnetwork employs virtual network elements (VNEs) 330, 332, 334, etc. thatperform some or all of the functions of network elements 150, 152, 154,156, etc. For example, the network architecture can provide a substrateof networking capability, often called Network Function VirtualizationInfrastructure (NFVI) or simply infrastructure that is capable of beingdirected with software and Software Defined Networking (SDN) protocolsto perform a broad variety of network functions and services. Thisinfrastructure can include several types of substrates. The most typicaltype of substrate being servers that support Network FunctionVirtualization (NFV), followed by packet forwarding capabilities basedon generic computing resources, with specialized network technologiesbrought to bear when general purpose processors or general purposeintegrated circuit devices offered by merchants (referred to herein asmerchant silicon) are not appropriate. In this case, communicationservices can be implemented as cloud-centric workloads.

As an example, a traditional network element 150 (shown in FIG. 1 ),such as an edge router can be implemented via a VNE 330 composed of NFVsoftware modules, merchant silicon, and associated controllers. Thesoftware can be written so that increasing workload consumes incrementalresources from a common resource pool, and moreover so that it'selastic: so the resources are only consumed when needed. In a similarfashion, other network elements such as other routers, switches, edgecaches, and middle-boxes are instantiated from the common resource pool.Such sharing of infrastructure across a broad set of uses makes planningand growing infrastructure easier to manage.

In an embodiment, the transport layer 350 includes fiber, cable, wiredand/or wireless transport elements, network elements and interfaces toprovide broadband access 110, wireless access 120, voice access 130,media access 140 and/or access to content sources 175 for distributionof content to any or all of the access technologies. In particular, insome cases a network element needs to be positioned at a specific place,and this allows for less sharing of common infrastructure. Other times,the network elements have specific physical layer adapters that cannotbe abstracted or virtualized, and might require special DSP code andanalog front-ends (AFEs) that do not lend themselves to implementationas VNEs 330, 332 or 334. These network elements can be included intransport layer 350.

The virtualized network function cloud 325 interfaces with the transportlayer 350 to provide the VNEs 330, 332, 334, etc. to provide specificNFVs. In particular, the virtualized network function cloud 325leverages cloud operations, applications, and architectures to supportnetworking workloads. The VNEs 330, 332 and 334 can employ networkfunction software that provides either a one-for-one mapping oftraditional network element function or alternately some combination ofnetwork functions designed for cloud computing. For example, VNEs 330,332 and 334 can include route reflectors, domain name system (DNS)servers, and dynamic host configuration protocol (DHCP) servers, systemarchitecture evolution (SAE) and/or mobility management entity (MME)gateways, broadband network gateways, IP edge routers for IP-VPN,Ethernet and other services, load balancers, distributers and othernetwork elements. Because these elements don't typically need to forwardlarge amounts of traffic, their workload can be distributed across anumber of servers—each of which adds a portion of the capability, andoverall which creates an elastic function with higher availability thanits former monolithic version. These VNEs 330, 332, 334, etc. can beinstantiated and managed using an orchestration approach similar tothose used in cloud compute services.

The cloud computing environments 375 can interface with the virtualizednetwork function cloud 325 via APIs that expose functional capabilitiesof the VNEs 330, 332, 334, etc. to provide the flexible and expandedcapabilities to the virtualized network function cloud 325. Inparticular, network workloads may have applications distributed acrossthe virtualized network function cloud 325 and cloud computingenvironment 375 and in the commercial cloud, or might simply orchestrateworkloads supported entirely in NFV infrastructure from these thirdparty locations.

Turning now to FIG. 4 , there is illustrated a block diagram of acomputing environment in accordance with various aspects describedherein. In order to provide additional context for various embodimentsof the embodiments described herein, FIG. 4 and the following discussionare intended to provide a brief, general description of a suitablecomputing environment 400 in which the various embodiments of thesubject disclosure can be implemented. In particular, computingenvironment 400 can be used in the implementation of network elements150, 152, 154, 156, access terminal 112, base station or access point122, switching device 132, media terminal 142, and/or VNEs 330, 332,334, etc. Each of these devices can be implemented viacomputer-executable instructions that can run on one or more computers,and/or in combination with other program modules and/or as a combinationof hardware and software.

Generally, program modules comprise routines, programs, components, datastructures, etc., that perform particular tasks or implement particularabstract data types. Moreover, those skilled in the art will appreciatethat the inventive methods can be practiced with other computer systemconfigurations, comprising single-processor or multiprocessor computersystems, minicomputers, mainframe computers, as well as personalcomputers, hand-held computing devices, microprocessor-based orprogrammable consumer electronics, and the like, each of which can beoperatively coupled to one or more associated devices.

As used herein, a processing circuit includes one or more processors aswell as other application specific circuits such as an applicationspecific integrated circuit, digital logic circuit, state machine,programmable gate array or other circuit that processes input signals ordata and that produces output signals or data in response thereto. Itshould be noted that while any functions and features described hereinin association with the operation of a processor could likewise beperformed by a processing circuit.

The illustrated embodiments of the embodiments herein can be alsopracticed in distributed computing environments where certain tasks areperformed by remote processing devices that are linked through acommunications network. In a distributed computing environment, programmodules can be located in both local and remote memory storage devices.

Computing devices typically comprise a variety of media, which cancomprise computer-readable storage media and/or communications media,which two terms are used herein differently from one another as follows.Computer-readable storage media can be any available storage media thatcan be accessed by the computer and comprises both volatile andnonvolatile media, removable and non-removable media. By way of example,and not limitation, computer-readable storage media can be implementedin connection with any method or technology for storage of informationsuch as computer-readable instructions, program modules, structured dataor unstructured data.

Computer-readable storage media can comprise, but are not limited to,random access memory (RAM), read only memory (ROM), electricallyerasable programmable read only memory (EEPROM), flash memory or othermemory technology, compact disk read only memory (CD-ROM), digitalversatile disk (DVD) or other optical disk storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devicesor other tangible and/or non-transitory media which can be used to storedesired information. In this regard, the terms “tangible” or“non-transitory” herein as applied to storage, memory orcomputer-readable media, are to be understood to exclude onlypropagating transitory signals per se as modifiers and do not relinquishrights to all standard storage, memory or computer-readable media thatare not only propagating transitory signals per se.

Computer-readable storage media can be accessed by one or more local orremote computing devices, e.g., via access requests, queries or otherdata retrieval protocols, for a variety of operations with respect tothe information stored by the medium.

Communications media typically embody computer-readable instructions,data structures, program modules or other structured or unstructureddata in a data signal such as a modulated data signal, e.g., a carrierwave or other transport mechanism, and comprises any informationdelivery or transport media. The term “modulated data signal” or signalsrefers to a signal that has one or more of its characteristics set orchanged in such a manner as to encode information in one or moresignals. By way of example, and not limitation, communication mediacomprise wired media, such as a wired network or direct-wiredconnection, and wireless media such as acoustic, RF, infrared and otherwireless media.

With reference again to FIG. 4 , the example environment can comprise acomputer 402, the computer 402 comprising a processing unit 404, asystem memory 406 and a system bus 408. The system bus 408 couplessystem components including, but not limited to, the system memory 406to the processing unit 404. The processing unit 404 can be any ofvarious commercially available processors. Dual microprocessors andother multiprocessor architectures can also be employed as theprocessing unit 404. The devices and nodes in system 200 in FIG. 2A andthe systems in FIGS. 2H-2M can comprise computer 402.

The system bus 408 can be any of several types of bus structure that canfurther interconnect to a memory bus (with or without a memorycontroller), a peripheral bus, and a local bus using any of a variety ofcommercially available bus architectures. The system memory 406comprises ROM 410 and RAM 412. A basic input/output system (BIOS) can bestored in a non-volatile memory such as ROM, erasable programmable readonly memory (EPROM), EEPROM, which BIOS contains the basic routines thathelp to transfer information between elements within the computer 402,such as during startup. The RAM 412 can also comprise a high-speed RAMsuch as static RAM for caching data.

The computer 402 further comprises an internal hard disk drive (HDD) 414(e.g., EIDE, SATA), which internal HDD 414 can also be configured forexternal use in a suitable chassis (not shown), a magnetic floppy diskdrive (FDD) 416, (e.g., to read from or write to a removable diskette418) and an optical disk drive 420, (e.g., reading a CD-ROM disk 422 or,to read from or write to other high capacity optical media such as theDVD). The HDD 414, magnetic FDD 416 and optical disk drive 420 can beconnected to the system bus 408 by a hard disk drive interface 424, amagnetic disk drive interface 426 and an optical drive interface 428,respectively. The hard disk drive interface 424 for external driveimplementations comprises at least one or both of Universal Serial Bus(USB) and Institute of Electrical and Electronics Engineers (IEEE) 1394interface technologies. Other external drive connection technologies arewithin contemplation of the embodiments described herein.

The drives and their associated computer-readable storage media providenonvolatile storage of data, data structures, computer-executableinstructions, and so forth. For the computer 402, the drives and storagemedia accommodate the storage of any data in a suitable digital format.Although the description of computer-readable storage media above refersto a hard disk drive (HDD), a removable magnetic diskette, and aremovable optical media such as a CD or DVD, it should be appreciated bythose skilled in the art that other types of storage media which arereadable by a computer, such as zip drives, magnetic cassettes, flashmemory cards, cartridges, and the like, can also be used in the exampleoperating environment, and further, that any such storage media cancontain computer-executable instructions for performing the methodsdescribed herein.

A number of program modules can be stored in the drives and RAM 412,comprising an operating system 430, one or more application programs432, other program modules 434 and program data 436. All or portions ofthe operating system, applications, modules, and/or data can also becached in the RAM 412. The systems and methods described herein can beimplemented utilizing various commercially available operating systemsor combinations of operating systems.

A user can enter commands and information into the computer 402 throughone or more wired/wireless input devices, e.g., a keyboard 438 and apointing device, such as a mouse 440. Other input devices (not shown)can comprise a microphone, an infrared (IR) remote control, a joystick,a game pad, a stylus pen, touch screen or the like. These and otherinput devices are often connected to the processing unit 404 through aninput device interface 442 that can be coupled to the system bus 408,but can be connected by other interfaces, such as a parallel port, anIEEE 1394 serial port, a game port, a universal serial bus (USB) port,an IR interface, etc.

A monitor 444 or other type of display device can be also connected tothe system bus 408 via an interface, such as a video adapter 446. Itwill also be appreciated that in alternative embodiments, a monitor 444can also be any display device (e.g., another computer having a display,a smart phone, a tablet computer, etc.) for receiving displayinformation associated with computer 402 via any communication means,including via the Internet and cloud-based networks. In addition to themonitor 444, a computer typically comprises other peripheral outputdevices (not shown), such as speakers, printers, etc.

The computer 402 can operate in a networked environment using logicalconnections via wired and/or wireless communications to one or moreremote computers, such as a remote computer(s) 448. The remotecomputer(s) 448 can be a workstation, a server computer, a router, apersonal computer, portable computer, microprocessor-based entertainmentappliance, a peer device or other common network node, and typicallycomprises many or all of the elements described relative to the computer402, although, for purposes of brevity, only a remote memory/storagedevice 450 is illustrated. The logical connections depicted comprisewired/wireless connectivity to a local area network (LAN) 452 and/orlarger networks, e.g., a wide area network (WAN) 454. Such LAN and WANnetworking environments are commonplace in offices and companies, andfacilitate enterprise-wide computer networks, such as intranets, all ofwhich can connect to a global communications network, e.g., theInternet.

When used in a LAN networking environment, the computer 402 can beconnected to the LAN 452 through a wired and/or wireless communicationnetwork interface or adapter 456. The adapter 456 can facilitate wiredor wireless communication to the LAN 452, which can also comprise awireless AP disposed thereon for communicating with the adapter 456.

When used in a WAN networking environment, the computer 402 can comprisea modem 458 or can be connected to a communications server on the WAN454 or has other means for establishing communications over the WAN 454,such as by way of the Internet. The modem 458, which can be internal orexternal and a wired or wireless device, can be connected to the systembus 408 via the input device interface 442. In a networked environment,program modules depicted relative to the computer 402 or portionsthereof, can be stored in the remote memory/storage device 450. It willbe appreciated that the network connections shown are example and othermeans of establishing a communications link between the computers can beused.

The computer 402 can be operable to communicate with any wirelessdevices or entities operatively disposed in wireless communication,e.g., a printer, scanner, desktop and/or portable computer, portabledata assistant, communications satellite, any piece of equipment orlocation associated with a wirelessly detectable tag (e.g., a kiosk,news stand, restroom), and telephone. This can comprise WirelessFidelity (Wi-Fi) and BLUETOOTH® wireless technologies. Thus, thecommunication can be a predefined structure as with a conventionalnetwork or simply an ad hoc communication between at least two devices.

Wi-Fi can allow connection to the Internet from a couch at home, a bedin a hotel room or a conference room at work, without wires. Wi-Fi is awireless technology similar to that used in a cell phone that enablessuch devices, e.g., computers, to send and receive data indoors and out;anywhere within the range of a base station. Wi-Fi networks use radiotechnologies called IEEE 802.11(a, b, g, n, ac, ag, etc.) to providesecure, reliable, fast wireless connectivity. A Wi-Fi network can beused to connect computers to each other, to the Internet, and to wirednetworks (which can use IEEE 802.3 or Ethernet). Wi-Fi networks operatein the unlicensed 2.4 and 5 GHz radio bands for example or with productsthat contain both bands (dual band), so the networks can providereal-world performance similar to the basic 10BaseT wired Ethernetnetworks used in many offices.

Turning now to FIG. 5 , an embodiment 500 of a mobile network platform510 is shown that is an example of network elements 150, 152, 154, 156,and/or VNEs 330, 332, 334, etc. System 200 in FIG. 2A and the systems inFIGS. 2H-2M can be located in mobile network platform 510 and implementmethod 260 as described herein.

In one or more embodiments, the mobile network platform 510 can generateand receive signals transmitted and received by base stations or accesspoints such as base station or access point 122. Generally, mobilenetwork platform 510 can comprise components, e.g., nodes, gateways,interfaces, servers, or disparate platforms, that facilitate bothpacket-switched (PS) (e.g., internet protocol (IP), frame relay,asynchronous transfer mode (ATM)) and circuit-switched (CS) traffic(e.g., voice and data), as well as control generation for networkedwireless telecommunication. As a non-limiting example, mobile networkplatform 510 can be included in telecommunications carrier networks, andcan be considered carrier-side components as discussed elsewhere herein.Mobile network platform 510 comprises CS gateway node(s) 512 which caninterface CS traffic received from legacy networks like telephonynetwork(s) 540 (e.g., public switched telephone network (PSTN), orpublic land mobile network (PLMN)) or a signaling system #7 (SS7)network 560. CS gateway node(s) 512 can authorize and authenticatetraffic (e.g., voice) arising from such networks. Additionally, CSgateway node(s) 512 can access mobility, or roaming, data generatedthrough SS7 network 560; for instance, mobility data stored in a visitedlocation register (VLR), which can reside in memory 530. Moreover, CSgateway node(s) 512 interfaces CS-based traffic and signaling and PSgateway node(s) 518. As an example, in a 3GPP UMTS network, CS gatewaynode(s) 512 can be realized at least in part in gateway GPRS supportnode(s) (GGSN). It should be appreciated that functionality and specificoperation of CS gateway node(s) 512, PS gateway node(s) 518, and servingnode(s) 516, is provided and dictated by radio technology(ies) utilizedby mobile network platform 510 for telecommunication over a radio accessnetwork 520 with other devices, such as radiotelephone 575.

In addition to receiving and processing CS-switched traffic andsignaling, PS gateway node(s) 518 can authorize and authenticatePS-based data sessions with served mobile devices. Data sessions cancomprise traffic, or content(s), exchanged with networks external to themobile network platform 510, like wide area network(s) (WAN) 550,enterprise network(s) 570, and service network(s) 580, which can beembodied in local area network(s) (LANs), can also be interfaced withmobile network platform 510 through PS gateway node(s) 518. It is to benoted that WAN 550 and enterprise network(s) 570 can embody, at least inpart, a service network(s) like IP multimedia subsystem (IMS). Based onradio technology layer(s) available in technology resource(s) of radioaccess network 520, PS gateway node(s) 518 can generate packet dataprotocol contexts when a data session is established; other datastructures that facilitate routing of packetized data also can begenerated. To that end, in an aspect, PS gateway node(s) 518 cancomprise a tunnel interface (e.g., tunnel termination gateway (TTG) in3GPP UMTS network(s) (not shown)) which can facilitate packetizedcommunication with disparate wireless network(s), such as Wi-Finetworks.

In embodiment 500, mobile network platform 510 also comprises servingnode(s) 516 that, based upon available radio technology layer(s) withintechnology resource(s) in the radio access network 520, convey thevarious packetized flows of data streams received through PS gatewaynode(s) 518. It is to be noted that for technology resource(s) that relyprimarily on CS communication, server node(s) can deliver trafficwithout reliance on PS gateway node(s) 518; for example, server node(s)can embody at least in part a mobile switching center. As an example, ina 3GPP UMTS network, serving node(s) 516 can be embodied in serving GPRSsupport node(s) (SGSN).

For radio technologies that exploit packetized communication, server(s)514 in mobile network platform 510 can execute numerous applicationsthat can generate multiple disparate packetized data streams or flows,and manage (e.g., schedule, queue, format . . . ) such flows. Suchapplication(s) can comprise add-on features to standard services (forexample, provisioning, billing, customer support . . . ) provided bymobile network platform 510. Data streams (e.g., content(s) that arepart of a voice call or data session) can be conveyed to PS gatewaynode(s) 518 for authorization/authentication and initiation of a datasession, and to serving node(s) 516 for communication thereafter. Inaddition to application server, server(s) 514 can comprise utilityserver(s), a utility server can comprise a provisioning server, anoperations and maintenance server, a security server that can implementat least in part a certificate authority and firewalls as well as othersecurity mechanisms, and the like. In an aspect, security server(s)secure communication served through mobile network platform 510 toensure network's operation and data integrity in addition toauthorization and authentication procedures that CS gateway node(s) 512and PS gateway node(s) 518 can enact. Moreover, provisioning server(s)can provision services from external network(s) like networks operatedby a disparate service provider; for instance, WAN 550 or GlobalPositioning System (GPS) network(s) (not shown). Provisioning server(s)can also provision coverage through networks associated to mobilenetwork platform 510 (e.g., deployed and operated by the same serviceprovider), such as the distributed antennas networks shown in FIG. 1(s)that enhance wireless service coverage by providing more networkcoverage.

It is to be noted that server(s) 514 can comprise one or more processorsconfigured to confer at least in part the functionality of mobilenetwork platform 510. To that end, the one or more processor can executecode instructions stored in memory 530, for example. It is should beappreciated that server(s) 514 can comprise a content manager, whichoperates in substantially the same manner as described hereinbefore.

In example embodiment 500, memory 530 can store information related tooperation of mobile network platform 510. Other operational informationcan comprise provisioning information of mobile devices served throughmobile network platform 510, subscriber databases; applicationintelligence, pricing schemes, e.g., promotional rates, flat-rateprograms, couponing campaigns; technical specification(s) consistentwith telecommunication protocols for operation of disparate radio, orwireless, technology layers; and so forth. Memory 530 can also storeinformation from at least one of telephony network(s) 540, WAN 550, SS7network 560, or enterprise network(s) 570. In an aspect, memory 530 canbe, for example, accessed as part of a data store component or as aremotely connected memory store.

In order to provide a context for the various aspects of the disclosedsubject matter, FIG. 5 , and the following discussion, are intended toprovide a brief, general description of a suitable environment in whichthe various aspects of the disclosed subject matter can be implemented.While the subject matter has been described above in the general contextof computer-executable instructions of a computer program that runs on acomputer and/or computers, those skilled in the art will recognize thatthe disclosed subject matter also can be implemented in combination withother program modules. Generally, program modules comprise routines,programs, components, data structures, etc. that perform particulartasks and/or implement particular abstract data types.

Turning now to FIG. 6 , an illustrative embodiment of a communicationdevice 600 is shown. The communication device 600 can comprise the nodesand devices in system 200 in FIG. 2A and the systems in FIGS. 2H-2M asdescribed herein.

The communication device 600 can serve as an illustrative embodiment ofdevices such as data terminals 114, mobile devices 124, vehicle 126,display devices 144 or other client devices for communication via eithercommunications network 125.

The communication device 600 can comprise a wireline and/or wirelesstransceiver 602 (herein transceiver 602), a user interface (UI) 604, apower supply 614, a location receiver 616, a motion sensor 618, anorientation sensor 620, and a controller 606 for managing operationsthereof. The transceiver 602 can support short-range or long-rangewireless access technologies such as Bluetooth®, ZigBee®, WiFi, DECT, orcellular communication technologies, just to mention a few (Bluetooth®and ZigBee® are trademarks registered by the Bluetooth® Special InterestGroup and the ZigBee® Alliance, respectively). Cellular technologies caninclude, for example, CDMA-1×, UMTS/HSDPA, GSM/GPRS, TDMA/EDGE, EV/DO,WiMAX, SDR, LTE, as well as other next generation wireless communicationtechnologies as they arise. The transceiver 602 can also be adapted tosupport circuit-switched wireline access technologies (such as PSTN),packet-switched wireline access technologies (such as TCP/IP, VoIP,etc.), and combinations thereof.

The UI 604 can include a depressible or touch-sensitive keypad 608 witha navigation mechanism such as a roller ball, a joystick, a mouse, or anavigation disk for manipulating operations of the communication device600. The keypad 608 can be an integral part of a housing assembly of thecommunication device 600 or an independent device operably coupledthereto by a tethered wireline interface (such as a USB cable) or awireless interface supporting for example Bluetooth®. The keypad 608 canrepresent a numeric keypad commonly used by phones, and/or a QWERTYkeypad with alphanumeric keys. The UI 604 can further include a display610 such as monochrome or color LCD (Liquid Crystal Display), OLED(Organic Light Emitting Diode) or other suitable display technology forconveying images to an end user of the communication device 600. In anembodiment where the display 610 is touch-sensitive, a portion or all ofthe keypad 608 can be presented by way of the display 610 withnavigation features.

The display 610 can use touch screen technology to also serve as a userinterface for detecting user input. As a touch screen display, thecommunication device 600 can be adapted to present a user interfacehaving graphical user interface (GUI) elements that can be selected by auser with a touch of a finger. The display 610 can be equipped withcapacitive, resistive or other forms of sensing technology to detect howmuch surface area of a user's finger has been placed on a portion of thetouch screen display. This sensing information can be used to controlthe manipulation of the GUI elements or other functions of the userinterface. The display 610 can be an integral part of the housingassembly of the communication device 600 or an independent devicecommunicatively coupled thereto by a tethered wireline interface (suchas a cable) or a wireless interface.

The UI 604 can also include an audio system 612 that utilizes audiotechnology for conveying low volume audio (such as audio heard inproximity of a human ear) and high volume audio (such as speakerphonefor hands free operation). The audio system 612 can further include amicrophone for receiving audible signals of an end user. The audiosystem 612 can also be used for voice recognition applications. The UI604 can further include an image sensor 613 such as a charged coupleddevice (CCD) camera for capturing still or moving images.

The power supply 614 can utilize common power management technologiessuch as replaceable and rechargeable batteries, supply regulationtechnologies, and/or charging system technologies for supplying energyto the components of the communication device 600 to facilitatelong-range or short-range portable communications. Alternatively, or incombination, the charging system can utilize external power sources suchas DC power supplied over a physical interface such as a USB port orother suitable tethering technologies.

The location receiver 616 can utilize location technology such as aglobal positioning system (GPS) receiver capable of assisted GPS foridentifying a location of the communication device 600 based on signalsgenerated by a constellation of GPS satellites, which can be used forfacilitating location services such as navigation. The motion sensor 618can utilize motion sensing technology such as an accelerometer, agyroscope, or other suitable motion sensing technology to detect motionof the communication device 600 in three-dimensional space. Theorientation sensor 620 can utilize orientation sensing technology suchas a magnetometer to detect the orientation of the communication device600 (north, south, west, and east, as well as combined orientations indegrees, minutes, or other suitable orientation metrics).

The communication device 600 can use the transceiver 602 to alsodetermine a proximity to a cellular, WiFi, Bluetooth®, or other wirelessaccess points by sensing techniques such as utilizing a received signalstrength indicator (RSSI) and/or signal time of arrival (TOA) or time offlight (TOF) measurements. The controller 606 can utilize computingtechnologies such as a microprocessor, a digital signal processor (DSP),programmable gate arrays, application specific integrated circuits,and/or a video processor with associated storage memory such as Flash,ROM, RAM, SRAM, DRAM or other storage technologies for executingcomputer instructions, controlling, and processing data supplied by theaforementioned components of the communication device 600.

Other components not shown in FIG. 6 can be used in one or moreembodiments of the subject disclosure. For instance, the communicationdevice 600 can include a slot for adding or removing an identity modulesuch as a Subscriber Identity Module (SIM) card or Universal IntegratedCircuit Card (UICC). SIM or UICC cards can be used for identifyingsubscriber services, executing programs, storing subscriber data, and soon.

The terms “first,” “second,” “third,” and so forth, as used in theclaims, unless otherwise clear by context, is for clarity only anddoesn't otherwise indicate or imply any order in time. For instance, “afirst determination,” “a second determination,” and “a thirddetermination,” does not indicate or imply that the first determinationis to be made before the second determination, or vice versa, etc.

In the subject specification, terms such as “store,” “storage,” “datastore,” data storage,” “database,” and substantially any otherinformation storage component relevant to operation and functionality ofa component, refer to “memory components,” or entities embodied in a“memory” or components comprising the memory. It will be appreciatedthat the memory components described herein can be either volatilememory or nonvolatile memory, or can comprise both volatile andnonvolatile memory, by way of illustration, and not limitation, volatilememory, non-volatile memory, disk storage, and memory storage. Further,nonvolatile memory can be included in read only memory (ROM),programmable ROM (PROM), electrically programmable ROM (EPROM),electrically erasable ROM (EEPROM), or flash memory. Volatile memory cancomprise random access memory (RAM), which acts as external cachememory. By way of illustration and not limitation, RAM is available inmany forms such as synchronous RAM (SRAM), dynamic RAM (DRAM),synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhancedSDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and direct Rambus RAM (DRRAM).Additionally, the disclosed memory components of systems or methodsherein are intended to comprise, without being limited to comprising,these and any other suitable types of memory.

Moreover, it will be noted that the disclosed subject matter can bepracticed with other computer system configurations, comprisingsingle-processor or multiprocessor computer systems, mini-computingdevices, mainframe computers, as well as personal computers, hand-heldcomputing devices (e.g., PDA, phone, smartphone, watch, tabletcomputers, netbook computers, etc.), microprocessor-based orprogrammable consumer or industrial electronics, and the like. Theillustrated aspects can also be practiced in distributed computingenvironments where tasks are performed by remote processing devices thatare linked through a communications network; however, some if not allaspects of the subject disclosure can be practiced on stand-alonecomputers. In a distributed computing environment, program modules canbe located in both local and remote memory storage devices.

Some of the embodiments described herein can also employ artificialintelligence (AI) to facilitate automating one or more featuresdescribed herein. The embodiments (e.g., in connection withautomatically identifying acquired cell sites that provide a maximumvalue/benefit after addition to an existing communication network) canemploy various AI-based schemes for carrying out various embodimentsthereof. Moreover, the classifier can be employed to determine a rankingor priority of each cell site of the acquired network. A classifier is afunction that maps an input attribute vector, x=(x1, x2, x3, x4, . . . ,xn), to a confidence that the input belongs to a class, that is,f(x)=confidence (class). Such classification can employ a probabilisticand/or statistical-based analysis (e.g., factoring into the analysisutilities and costs) to determine or infer an action that a user desiresto be automatically performed. A support vector machine (SVM) is anexample of a classifier that can be employed. The SVM operates byfinding a hypersurface in the space of possible inputs, which thehypersurface attempts to split the triggering criteria from thenon-triggering events. Intuitively, this makes the classificationcorrect for testing data that is near, but not identical to trainingdata. Other directed and undirected model classification approachescomprise, e.g., naïve Bayes, Bayesian networks, decision trees, neuralnetworks, fuzzy logic models, and probabilistic classification modelsproviding different patterns of independence can be employed.Classification as used herein also is inclusive of statisticalregression that is utilized to develop models of priority.

As will be readily appreciated, one or more of the embodiments canemploy classifiers that are explicitly trained (e.g., via a generictraining data) as well as implicitly trained (e.g., via observing UEbehavior, operator preferences, historical information, receivingextrinsic information). For example, SVMs can be configured via alearning or training phase within a classifier constructor and featureselection module. Thus, the classifier(s) can be used to automaticallylearn and perform a number of functions, including but not limited todetermining according to predetermined criteria which of the acquiredcell sites will benefit a maximum number of subscribers and/or which ofthe acquired cell sites will add minimum value to the existingcommunication network coverage, etc.

As used in some contexts in this application, in some embodiments, theterms “component,” “system” and the like are intended to refer to, orcomprise, a computer-related entity or an entity related to anoperational apparatus with one or more specific functionalities, whereinthe entity can be either hardware, a combination of hardware andsoftware, software, or software in execution. As an example, a componentmay be, but is not limited to being, a process running on a processor, aprocessor, an object, an executable, a thread of execution,computer-executable instructions, a program, and/or a computer. By wayof illustration and not limitation, both an application running on aserver and the server can be a component. One or more components mayreside within a process and/or thread of execution and a component maybe localized on one computer and/or distributed between two or morecomputers. In addition, these components can execute from variouscomputer readable media having various data structures stored thereon.The components may communicate via local and/or remote processes such asin accordance with a signal having one or more data packets (e.g., datafrom one component interacting with another component in a local system,distributed system, and/or across a network such as the Internet withother systems via the signal). As another example, a component can be anapparatus with specific functionality provided by mechanical partsoperated by electric or electronic circuitry, which is operated by asoftware or firmware application executed by a processor, wherein theprocessor can be internal or external to the apparatus and executes atleast a part of the software or firmware application. As yet anotherexample, a component can be an apparatus that provides specificfunctionality through electronic components without mechanical parts,the electronic components can comprise a processor therein to executesoftware or firmware that confers at least in part the functionality ofthe electronic components. While various components have beenillustrated as separate components, it will be appreciated that multiplecomponents can be implemented as a single component, or a singlecomponent can be implemented as multiple components, without departingfrom example embodiments.

Further, the various embodiments can be implemented as a method,apparatus or article of manufacture using standard programming and/orengineering techniques to produce software, firmware, hardware or anycombination thereof to control a computer to implement the disclosedsubject matter. The term “article of manufacture” as used herein isintended to encompass a computer program accessible from anycomputer-readable device or computer-readable storage/communicationsmedia. For example, computer readable storage media can include, but arenot limited to, magnetic storage devices (e.g., hard disk, floppy disk,magnetic strips), optical disks (e.g., compact disk (CD), digitalversatile disk (DVD)), smart cards, and flash memory devices (e.g.,card, stick, key drive). Of course, those skilled in the art willrecognize many modifications can be made to this configuration withoutdeparting from the scope or spirit of the various embodiments.

In addition, the words “example” and “exemplary” are used herein to meanserving as an instance or illustration. Any embodiment or designdescribed herein as “example” or “exemplary” is not necessarily to beconstrued as preferred or advantageous over other embodiments ordesigns. Rather, use of the word example or exemplary is intended topresent concepts in a concrete fashion. As used in this application, theterm “or” is intended to mean an inclusive “or” rather than an exclusive“or”. That is, unless specified otherwise or clear from context, “Xemploys A or B” is intended to mean any of the natural inclusivepermutations. That is, if X employs A; X employs B; or X employs both Aand B, then “X employs A or B” is satisfied under any of the foregoinginstances. In addition, the articles “a” and “an” as used in thisapplication and the appended claims should generally be construed tomean “one or more” unless specified otherwise or clear from context tobe directed to a singular form.

Moreover, terms such as “user equipment,” “mobile station,” “mobile,”subscriber station,” “access terminal,” “terminal,” “handset,” “mobiledevice” (and/or terms representing similar terminology) can refer to awireless device utilized by a subscriber or user of a wirelesscommunication service to receive or convey data, control, voice, video,sound, gaming or substantially any data-stream or signaling-stream. Theforegoing terms are utilized interchangeably herein and with referenceto the related drawings.

Furthermore, the terms “user,” “subscriber,” “customer,” “consumer” andthe like are employed interchangeably throughout, unless contextwarrants particular distinctions among the terms. It should beappreciated that such terms can refer to human entities or automatedcomponents supported through artificial intelligence (e.g., a capacityto make inference based, at least, on complex mathematical formalisms),which can provide simulated vision, sound recognition and so forth.

As employed herein, the term “processor” can refer to substantially anycomputing processing unit or device comprising, but not limited tocomprising, single-core processors; single-processors with softwaremultithread execution capability; multi-core processors; multi-coreprocessors with software multithread execution capability; multi-coreprocessors with hardware multithread technology; parallel platforms; andparallel platforms with distributed shared memory. Additionally, aprocessor can refer to an integrated circuit, an application specificintegrated circuit (ASIC), a digital signal processor (DSP), a fieldprogrammable gate array (FPGA), a programmable logic controller (PLC), acomplex programmable logic device (CPLD), a discrete gate or transistorlogic, discrete hardware components or any combination thereof designedto perform the functions described herein. Processors can exploitnano-scale architectures such as, but not limited to, molecular andquantum-dot based transistors, switches and gates, in order to optimizespace usage or enhance performance of user equipment. A processor canalso be implemented as a combination of computing processing units.

As used herein, terms such as “data storage,” data storage,” “database,”and substantially any other information storage component relevant tooperation and functionality of a component, refer to “memorycomponents,” or entities embodied in a “memory” or components comprisingthe memory. It will be appreciated that the memory components orcomputer-readable storage media, described herein can be either volatilememory or nonvolatile memory or can include both volatile andnonvolatile memory.

What has been described above includes mere examples of variousembodiments. It is, of course, not possible to describe everyconceivable combination of components or methodologies for purposes ofdescribing these examples, but one of ordinary skill in the art canrecognize that many further combinations and permutations of the presentembodiments are possible. Accordingly, the embodiments disclosed and/orclaimed herein are intended to embrace all such alterations,modifications and variations that fall within the spirit and scope ofthe appended claims. Furthermore, to the extent that the term “includes”is used in either the detailed description or the claims, such term isintended to be inclusive in a manner similar to the term “comprising” as“comprising” is interpreted when employed as a transitional word in aclaim.

In addition, a flow diagram may include a “start” and/or “continue”indication. The “start” and “continue” indications reflect that thesteps presented can optionally be incorporated in or otherwise used inconjunction with other routines. In this context, “start” indicates thebeginning of the first step presented and may be preceded by otheractivities not specifically shown. Further, the “continue” indicationreflects that the steps presented may be performed multiple times and/ormay be succeeded by other activities not specifically shown. Further,while a flow diagram indicates a particular ordering of steps, otherorderings are likewise possible provided that the principles ofcausality are maintained.

As may also be used herein, the term(s) “operably coupled to”, “coupledto”, and/or “coupling” includes direct coupling between items and/orindirect coupling between items via one or more intervening items. Suchitems and intervening items include, but are not limited to, junctions,communication paths, components, circuit elements, circuits, functionalblocks, and/or devices. As an example of indirect coupling, a signalconveyed from a first item to a second item may be modified by one ormore intervening items by modifying the form, nature or format ofinformation in a signal, while one or more elements of the informationin the signal are nevertheless conveyed in a manner than can berecognized by the second item. In a further example of indirectcoupling, an action in a first item can cause a reaction on the seconditem, as a result of actions and/or reactions in one or more interveningitems.

Although specific embodiments have been illustrated and describedherein, it should be appreciated that any arrangement which achieves thesame or similar purpose may be substituted for the embodiments describedor shown by the subject disclosure. The subject disclosure is intendedto cover any and all adaptations or variations of various embodiments.Combinations of the above embodiments, and other embodiments notspecifically described herein, can be used in the subject disclosure.For instance, one or more features from one or more embodiments can becombined with one or more features of one or more other embodiments. Inone or more embodiments, features that are positively recited can alsobe negatively recited and excluded from the embodiment with or withoutreplacement by another structural and/or functional feature. The stepsor functions described with respect to the embodiments of the subjectdisclosure can be performed in any order. The steps or functionsdescribed with respect to the embodiments of the subject disclosure canbe performed alone or in combination with other steps or functions ofthe subject disclosure, as well as from other embodiments or from othersteps that have not been described in the subject disclosure. Further,more than or less than all of the features described with respect to anembodiment can also be utilized.

What is claimed is:
 1. A method, comprising: iteratively providing, froma message handler of a processing system including a processor, a firstmessage to each of a group of node processors of the processing systemresulting in a group of first messages, wherein each of the group ofnode processors represents a node of a group of nodes, and wherein theiteratively providing of the group of first messages comprises:selecting, by the message handler, at least one path from a first groupof paths associated with a known minimum solution (KMS) from a firstgroup of costs resulting in at least one first selected path; andproviding, by the message handler, a next message that includes the atleast one first selected path to a first portion of the group of nodeprocessors of the processing system resulting in a first group of nextmessages and a first plurality of selected paths; and responsive to theiteratively providing of the group of first messages and first group ofnext messages, determining, by the message handler, a first target paththat is a remaining path of the first plurality of selected paths,wherein the remaining path is identified from the iteratively providingof the group of first messages and the first group of next messages. 2.The method of claim 1, further comprising identifying, by the messagehandler, the KMS.
 3. The method of claim 2, wherein the KMS is a leastcost from the first group of costs.
 4. The method of claim 1, furthercomprising determining, by the message handler, a plurality of costsassociated with a plurality of paths for each first message in the groupof first messages resulting in the first group of costs and the firstgroup of paths.
 5. The method of claim 4, wherein the plurality of costscomprise time, distance, monetary cost, available bandwidth, latency,throughput, risk, probability of success, or any combination thereof. 6.The method of claim 1, wherein the first target path is through eachnode of the group of nodes.
 7. The method of claim 1, comprising:determining, by the message handler, an average cost between any twonodes of the group of nodes, and determining, by the message handler, astandard deviation associated with the average cost.
 8. The method ofclaim 7, wherein the selecting the at least one path from the firstgroup of paths associated with the KMS comprises selecting, by themessage handler, the at least one path from the first group of pathsaccording to the average cost and the standard deviation.
 9. The methodof claim 7, comprising identifying, by the message handler, a firstportion of the first group of paths such that each of the first portionof the first group of paths is associated with a first cost that is morethan the average cost and the standard deviation associated with theaverage cost resulting in a first identification of a group ofsequestered paths.
 10. The method of claim 9, comprising providing, bythe message handler, the first identification of the group ofsequestered paths to a sequestration handler, wherein the processingsystem comprises the sequestration handler.
 11. The method of claim 1,wherein the first target path is a complete path.
 12. The method ofclaim 1, wherein the first target path is a complete shortest path. 13.A device, comprising: a processing system including a processor, a groupof node processors, an administration processor, and a message handler,wherein each of the group of node processors represents a node of agroup of nodes; and a memory that stores executable instructions that,when executed by the processing system, facilitates performance ofoperations, the operations comprising: iteratively providing a firstmessage to each of a group of node processors of the processing systemresulting in a group of first messages, wherein each of the group ofnode processors represents a node of a group of nodes, wherein theiteratively providing of the group of first messages comprises:selecting at least one path from a first group of paths associated witha known minimum solution (KMS) from a first group of costs resulting inat least one first selected path; and providing a next message thatincludes the at least one first selected path to a first portion of thegroup of node processors of the processing system resulting in a firstgroup of next messages and a first plurality of selected paths; andresponsive to the iteratively providing of the group of first messagesand first group of next messages, determining a first target path thatis a remaining path of the first plurality of selected paths.
 14. Thedevice of claim 13, wherein the remaining path is identified from theiteratively providing of the group of first messages and the first groupof next messages.
 15. The device of claim 13, wherein the operationsfurther comprise identifying the KMS, wherein the KMS is a least costfrom the first group of costs.
 16. The device of claim 13, wherein theoperations further comprise determining a plurality of costs associatedwith a plurality of paths for each first message in the group of firstmessages resulting in the first group of costs and the first group ofpaths, wherein the plurality of costs comprise time, distance, monetarycost, available bandwidth, latency, throughput, risk, probability ofsuccess, or any combination thereof.
 17. The device of claim 13, whereinthe first target path is through each node of the group of nodes.
 18. Anon-transitory, machine-readable medium, comprising executableinstructions that, when executed by a processing system including aprocessor, a group of node processors, an administration processor, anda message handler, facilitate performance of operations, the operationscomprising: iteratively providing a first message to each of a group ofnode processors of the processing system resulting in a group of firstmessages, wherein the iteratively providing of the group of firstmessages comprises: selecting at least one path from a first group ofpaths associated with a known minimum solution (KMS) from a first groupof costs resulting in at least one first selected path; and providing anext message that includes the at least one first selected path to afirst portion of the group of node processors of the processing systemresulting in a first group of next messages and a first plurality ofselected paths; and responsive to the iteratively providing of the groupof first messages and first group of next messages, determining a firsttarget path that is a remaining path of the first plurality of selectedpaths.
 19. The non-transitory, machine-readable medium of claim 18,wherein each of the group of node processors represents a node of agroup of nodes.
 20. The non-transitory, machine-readable medium of claim18, wherein the operations further comprise determining a plurality ofcosts associated with a plurality of paths for each first message in thegroup of first messages resulting in the first group of costs and thefirst group of paths.